Tsunami Assessment Method for
Nuclear Power Plants in Japan 2016

September 2016
The Tsunami Evaluation Subcommittee,
The Nuclear Civil Engineering Committee,
JSCE (Japan Society of Civil Engineers)Preface
The 2011 Tohoku earthquake (the 2011 off the Pacific coast of Tohoku Earthquake) , which struck
off the Pacific coast of the Tohoku region on March 11, 2011, possessed the greatest amount of energy
ever observed in an area around Japan. The earthquake recorded a moment magnitude of 9.0 with anextensive hypocentral region measuring 200km east to west and 500km north to south. Damage wasof an unprecedented scale. However, the extent of the damage attributable to ground vibration was
relatively small, and most of the human and economic damage resulted from the tsunami, which has
been described as being of a scale occurring once every thousand years. Among the damage inflicted,
the accident at Tokyo Electric Power Company’s Fukushima Daiichi Nuclear Power Station developed
into a severe accident that led to failure of the primary containment vessel, the first such experiencein Japan. The resulting variance of radioactive materials forced the evacuation of many people and left
a sizable scar on the land such that even today five years after the earthquake there are areas to whichpeople are not permitted to return.
The direct cause of this accident lies in the seawalls, which had been erected, not being able toperform their function against the strike of a tsunami that reached a height exceeding any previous
rendered assumptions and the resulting station blackout caused by inundation of seawater throughout
the site. In devising the assumptions that had been worked out for tsunami height at the Fukushima
Daiichi Nuclear Power Station, the “Tsunami Assessment Method for Nuclear Power Plants in Japan”,
published by the Japan Society of Civil Engineers in 2002, was utilized. Consequently, the engineers,
researchers and the Japan Society of Civil Engineers involved in putting together this publication were
subjected to criticism.
We, engineers and researchers, need to sincerely face the fact that we were unable to estimate thescale of the earthquake and tsunami that actually occurred, and to accept that our knowledge andjudgments were not insufficient. It is true that improvement of our geophysical knowledge waits upon
the development of various types of observation instruments, and that empirical research onmechanisms generating earthquakes only just began in the late 1960s. With respect to tsunami, themechanism for such occurrences is thought to depend significantly on the mechanism of earthquake
generation, and full-scale research in this field merely entered the initial phase in the late 1970s.
At the time of the release of the previously published “Tsunami Assessment Method for Nuclear
Power Plants in Japan”, the tsunami estimation technology was still under development, so the largest
ever recorded tsunami was used as the benchmark on the assumption that new knowledge would
subsequently be proactively incorporated. Of course, although this system took into accountuncertainty to a certain extent, the end result was that a variety of phenomena were not able to be taken
into account that occur in nuclear power plant systems when such a facility is struck by a tsunami
exceeding all previous expectations.
1

Academic advances with respect to tsunami are truly progressing at a rapid rate. Even since 2002,
much new knowledge has been gained and remarkable progress made in the numerical analysis
technology for predicting tsunami height. Unfortunately, before these developments were sufficiently
utilized, the 2011 Tohoku earthquake occurred. However, over the five years since the earthquake
occurred, we have been able to conduct detailed analyses of the conditions of this tsunami to verify
our previous knowledge, and we have also been able to raise the level of scholarship addressing
tsunami. These results have been compiled here in this publication “Tsunami Assessment Methods for
Nuclear Power Plants in Japan: 2016”. Our goal has not been to present the state of research andtechnology achievements accomplished up to a certain point, but to provide a starting point foradvancing scholarship the next step. We hope that this publication will lead to further development oftechnology for assessing tsunami.
We wish to express our deepest gratitude to Tomoyuki Takahashi, Chairman of the Tsunami
Evaluation Subcommittee as well as the committee members and Chief Secretary for their dedicatedefforts in putting together this publication.

September 2016
Kyuichi Maruyama, Chairman
The Nuclear Civil Engineering Committee

2

Usage of This Publication○ This publication is comprised of main volume and appendix volume, and these are a compilation ofassessment approaches for configuring hypothetical tsunami with respect to a nuclear power plant,
available elementary technologies and examples of such applications. The assessment approaches
and examples of such applications presented in this publication do not imply a universal maximum
scale of the various types of anticipated tsunami with the goal of preventing or reducing damage
inflicted by a tsunami on society, nor do they indicate a minimum required level for a hypotheticaltsunami. The Tsunami Evaluation Subcommittee under the auspices of the Japan Society of Civil
Engineers’ Nuclear Civil Engineering Committee believes that the various conditions necessary for
estimating tsunami should be configured for each individual case based on relevant knowledge inkeeping with the design objectives, use and other factors.
○ Any responsibility for damage or other harm to a third-party as well as damage that occurs from theuse of methods and procedures for assessing hypothetical tsunami as well as applicable case studies
presented in this publication lies with the user, and the Tsunami Evaluation Subcommittee under the
auspices of the Japan Society of Civil Engineers’ Nuclear Civil Engineering Committee as well as
any other person involved with the preparation of this publication shall assume no liability
whatsoever.

3Chapter 1 Preface
The 2011 Tohoku earthquake (the 2011 off the Pacific coast of Tohoku Earthquake), which struck
on March 11, 2011, inflicted enormous human loss and economic damage on Japan. A large part ofthis damage was due to the tsunami that far exceeded expectations. The tsunami, which battered
coastal regions, extended beyond those areas, where flooding had been anticipated and announced by
local municipalities, to swallow up thousands of people and homes. This tsunami disaster was a vivid
display of how an external force exceeding what has been anticipated considerably intensifies thedamage. Moreover, the tsunami flooded the site of the Fukushima Daiichi Nuclear Power Station, andwas the principal factor causing a major accident there. The damage from the nuclear accident has
extended across a very broad area and will continue to affect this area for a very long period of time.
We must seriously confront this grave accident and clarify the mechanisms that gave rise to it as wellas endeavor to prevent any such recurrence.
Although this accident involved a variety of factors, there is no mistake that the direct andproximate cause was the strike of a tsunami that far exceeded expectations. Put another way, the factthat the tsunami had been underestimated was a major cause of the accident. An equivalent or perhaps
even greater issue was that insufficient assumptions had been made about what condition the nuclear
power plant might lapse into when a tsunami that exceeded expectations hit, and preparations for sucha contingency were insufficient. In other words, the fact that the perspective of defense in depth waslacking also brought about even more extensive damage. We must earnestly address these two points
so that the lessons learned from the 2011 Tohoku earthquake may be put to good use in preventing
nuclear disasters in the future.
The Headquarters for Earthquake Research Promotion, Central Disaster Management Council,
local governments and other public institutions have already prepared several tsunami estimates, andthese tsunamis have been considered in assessments with respect to nuclear power plants. However,many of the estimates prior to the 2011 Tohoku earthquake were principally reproductions of thelargest recorded tsunami based on historical records, which were set as the standard even inconsiderations of uncertainty. However, the information about past tsunami that we have is not
sufficient, and the 2011 Tohoku earthquake showed that there are even larger tsunamis that we did notknow about. We need to humbly accept this fact, and not depend only on deterministic methods, butalso, in the future, articulate assessments of tsunami hazard based on probabilistic methods.
A lot of material has already been created on methods for assessing tsunami. Among these, the“Guide to Strengthening Tsunami Countermeasures in Regional Disaster Prevention Plans”, which
was published by seven government agencies concerned with coastal areas (National Land Agency,
Ministry of Agriculture, Forestry and Fisheries’ Agricultural Structure Improvement Bureau, Ministryof Agriculture, Forestry and Fisheries’ Fisheries Agency, Ministry of Transport, Japan Meteorological4Agency, Ministry of Construction, and the Fire and Disaster Management Agency) in March 1998,
provides a compilation of methods for surveying and assessing relevant tsunami, and constructed afoundation upon which tsunami damage is currently estimated. Moreover, the “Guide to Configurationof Tsunami Inundation Estimates”, which was published by the Ministry of Land, Infrastructure,
Transport and Tourism’s Water and Disaster Management Bureau’s Seacoast Office and the National
Institute for Land and Infrastructure Management’s River Department’s Coast Division in February
2012 after the 2011 Tohoku earthquake, provides a detailed compilation of methods and othertechniques for simulating tsunami inundation that is necessary when local governments undertake
efforts to estimate tsunami damage. These guides are applicable to general disaster prevention, but toaddress nuclear disaster prevention, the “Tsunami Assessment Method for Nuclear Power Plants inJapan”, the precursor to this publication, was released as a report issued by the Tsunami Evaluation
Subcommittee (then), the Nuclear Civil Engineering Committee, Japan Society of Civil Engineers in
February 2002. This report compiles a variety of knowledge obtained from previous research on
earthquakes and tsunami into a single work, and assembles methods available for configuring design
tsunami with respect to nuclear power plants. In addition, so that the publication may also be used in
the field where disaster prevention is practiced, analytical methods are explained in detail. As such, it
has been extensively utilized also in general disaster prevention. Subsequently, the publication“Methods of Probabilistic Tsunami Hazard Analysis” (Japan Society of Civil Engineers, 2011), which
provides techniques for assessing tsunami hazards based upon probability theory, was compiled. Thismethod has been incorporated into a technological standard (Atomic Energy Society of Japan, 2011)that sets forth the specifications and standards to serve as technical guidelines established by the
Atomic Energy Society of Japan.
More than 10 years have passed since the previous publication was released (in 2002), and much
new knowledge about earthquakes and tsunami has been gained. In addition, estimation methods andanalytical methods have also become more advanced and cover a broader range of events. The
Tsunami Assessment Panel changed its name to the Tsunami Evaluation Subcommittee in September
2013, but it has continued to study tsunami assessment technology for nuclear power plants.
Accordingly, the previous publication has been wholly revised, and knowledge about the 2011 Tohoku
earthquake has furthermore been taken into account in the release of this new publication. Along withassessments from the aforementioned perspective of defense in depth and probabilistic tsunami hazard
analyses, numerous items have been newly added, including methods for assessing non-earthquake
factors causing tsunami as well as methods for analyzing complex phenomena that arise along with atsunami strike, including tsunami force, sediment transport and flotsam. Just as with the previous
publication, this document brings together the most up-to-date available knowledge into a single
volume, compiling technologies for assessing tsunami with respect to nuclear power plants.
This publication includes assessment technology that may also be used for tsunami
5

countermeasures other than those specific to nuclear power plants. However, it is desirable to give
sufficient consideration also to the fact that tsunami countermeasure methods and approaches differ
depending on their purpose, role and scale.

[Chapter 1 References]
Atomic Energy Society of Japan (2011): Implementation Standard Concerning the Tsunami
Probabilistic Risk Assessment Due to Tsunami on Nuclear Power Plants, 2011(AESJ-SCRK004E:2011).
Japan Society of Civil Engineers Nuclear Civil Engineering Committee (2002): Tsunami Assessment
Method for Nuclear Power Plants in Japan.
Japan Society of Civil Engineers Nuclear Civil Engineering Committee (2011): Methods ofProbabilistic Tsunami Hazard Analysis, http://committees.jsce.or.jp/ceofnp/node/39(Accessed on August 2016).
Ministry of Land, Infrastructure, Transport and Tourism’s Water and Disaster Management Bureau’s
Seacoast Office and the National Institute for Land and Infrastructure Management’s River
Department’s Coast Division (2012): Guide to Configuration of Tsunami Inundation Estimates.
National Land Agency, Ministry of Agriculture, Forestry and Fisheries’ Agricultural Structure
Improvement Bureau, Ministry of Agriculture, Forestry and Fisheries’ Fisheries Agency,
Ministry of Transport, Japan Meteorological Agency, Ministry of Construction, and the Fireand Disaster Management Agency (1998): Guide to Strengthening Tsunami Countermeasuresin Regional Disaster Prevention Plans.

6Chapter 2 Overview of Tsunami Assessments
2.1 Lessons of the 2011 Tohoku Earthquake
At least when it occurred, the 2011 Tohoku earthquake was the most massive earthquake with amagnitude 9.0 or higher believed to have ever been encountered in Japan’s history, and the tsunamithat it brought about was enormous inflicting damage across a broad swath of the country. This tsunami
was gigantic, reaching a maximum run-up height of 40m, and the length of coastline where the tsunami
reached a height of 5m or greater spread across an extensive area of more than 500km. The tsunami’s
enormity and broad area of impact was on an unprecedented scale exceeding the tsunami caused by
the 1707 Hoei earthquake, which had been believed to have been the largest tsunami on record inJapan. The 2011 Tohoku earthquake and subsequent tsunami had a tremendous impact on nuclear
power stations along the Pacific coast, and brought about the accident at the Fukushima Daiichi
Nuclear Power Station where radioactive materials were released (hereinafter referred to as the“Fukushima Daiichi accident”). The principal cause of this accident is held to be inundation of thereactor building by seawater that ran up onto the site from the tsunami. This flooding resulted in astation blackout and the loss of safety system functions (Atomic Energy Society of Japan, 2014).
Following the Fukushima Daiichi accident, the Japan Society of Civil Engineers’ Nuclear Civil
Engineering Committee organized the Committee on Specific Topics Concerning Civil Engineering
Technology for Nuclear Safety, which held a series of deliberations that resulted in the presentation of
proposals on how nuclear safety should be structured against earthquakes, tsunami and other external
natural events (Committee on Specific Topics Concerning Civil Engineering Technology for Nuclear
Safety, 2013). The proposals first presented a concept that extends across the five tiers set out by theInternational Atomic Energy Agency (“IAEA”) regarding defense in depth, which is the basic
approach for nuclear safety (Figure 2.1-1). Next, the principal factor leading to the Fukushima Daiichi
accident was the breakdown of the third level of defense in depth “control of accidents in design basis”
due to the tsunami that exceeded the level serving as the standard for design. Furthermore, it has been
pointed out that there were no effective safety functions corresponding to the fourth level of defense
in depth “accident management and confinement of impact” in response to inundation by a tsunami
within the site or inside buildings. Accordingly, in the awareness of the possibility that an event mightoccur exceeding the seismic ground motion and tsunami that serve as the benchmark, a new capability
known as “Anti-Catastrophe” was proposed so that the fourth level of defense in depth is able tofunction effectively against such events. Resilience is the capability to sufficiently reduce thepossibility that a crisis situation may result across the entire nuclear power plant system by means ofemergency measures or other such means, even in situations where the external force set as thestandard has been exceeded. In order to ensure this “Anti-Catastrophe”, an understanding of the entire
7

system comprising a nuclear power plant is necessary as well as discussions transcending the barriers
between various engineering fields related to each system.
The Atomic Energy Society of Japan’s Investigation Committee on the Nuclear Accident at the
Fukushima Daiichi Nuclear Power Plant was organized for the purpose of analyzing the Fukushima
Daiichi accident and the actual circumstances of the subsequent nuclear disaster from a scientific andspecialized perspective to clarify the underlying and root causes as well as to propose an approach tosafety that would formulate measures, a foundation for ensuring nuclear safety and the achievementof continual safety improvements. The final report indicated that there were three direct accident
causes: inadequate response to a natural disaster, inadequate severe accident management measures,and confusion during the emergency response.
Based upon the aforementioned, the following two lessons were cited in hindsight with respect
to ensuring the safety of a nuclear power plant against a tsunami.
A) Preparations against a tsunami exceeding the design basis were insufficient.
B) The height of the tsunami water level which formed the design basis was insufficient.
In the Nuclear Reactor Regulation Act revised in 2013, additions were incorporated providing fora shift to safety regulations that also take into account major accidents and a shift to regulations that
also reflect the latest knowledge for existing facilities (backfit) (Nuclear Regulation Authority, 2013a).
The new regulatory requirements, which were reviewed and drafted following this legal revision, haveenshrined (1) the enhancement of measures against events, including those exceeding the design basis
so that a major accident will not result, and (2) the enhancement of measures against large-scale natural
disasters so that safety functions are not lost simultaneously. In addition to earthquakes and tsunami,
natural phenomena anticipated also included volcanic eruptions, tornadoes and other such events, and,with respect to tsunami, the measures also cover tsunami resulting from factors other than fault
movement. Numerals (1) and (2) corresponded respectively to the previously presented lessons learned(A) and (B), and are in harmony with the approach of ensuring anti-catastrophe.

8

Figure 2.1-1 IAEA defense in depth (Yamaguchi, 2012)
2.2 Background and Objectives of this Publication
Endeavoring to manage and reduce risks due to tsunami from the perspective of defense in depth
is a practical method for ensuring anti-catastrophe, in other words, ensuring nuclear safety. Table 2.21 provides an example of how design standards are situated in relation to defense in depth. Based on
this, three points are noted: (1) protection and control through the original design against events within
the design basis, and, furthermore, (2) prevention of escalation of an accident attributable to events
exceeding the design basis, and (3) mitigation of the impact of a major accident. Specific examples of
responses at each of these levels (1) through (3) are, with respect to (1): tide embankments and othertsunami protection facilities that reduce potential flooding accompanying a tsunami; with respect to(2): the prevention of inundation of buildings by improving the water tightness of building openings
in preparation for cases where the tsunami inundates a site as well as impact mitigation withalternatives in cases where electrical equipment or power supplies are impaired; and, with respect to(3): evacuation of residents and other nuclear disaster prevention measures.
With respect to examples (1) and (2) of the responses presented above, it is necessary to assess9the action of the tsunami, such as inundation, tsunami force, tsunami pressure and other properties andtheir impact on the respective pieces of equipment and machinery. To that end, in addition to a civilengineering field assessment of such actions, the knowledge of experts in a wide variety of fields,
including nuclear, mechanical and electrical, is necessary to assess such effects. In addition, theapproach to improving safety against earthquakes and tsunami with respect to nuclear power plants
and the course of such assessments has also been presented in the new regulatory standards, byscholarly societies and others (Atomic Energy Society of Japan, 2014; Kameda, 2011; Joint Editorial
Committee for the Reports on the Great East Japan Earthquake Disaster, 2013; Japan Association for
Earthquake Engineering, 2014). These deliberations are ongoing and will likely be updated in the
future as well. The IAEA has proposed the “Integrated Risk Informed Decision-Making (IRIDM)” toserve as the system for making decisions about measures addressing such issues. In so doing,
deterministic tsunami hazards and probabilistic tsunami risk hazards are utilized to provide
information about risks, which is necessary for rendering decisions about tsunami countermeasures(Figure 2.2-1, IAEA, 2011; Narumiya, 2014).
Accordingly, the objective of this publication is to compile deterministic tsunami hazard analysis,
probabilistic tsunami hazard analysis, methods for assessing the action of inundation, tsunami force,tsunami pressure and other properties attributable to tsunami, as well as the elemental technology
necessary for such methods, which are considered necessary when formulating an approach to
improving safety and constructing a course for assessments that will be updated as well in the future
to reflect the latest knowledge.
It is hoped that these elemental technologies will be utilized in the continuing enhancement ofassessments for improving safety as indicated in the Nuclear Reactor Regulation Act (Nuclear
Regulation Authority, 2013b), such as, for example, in probabilistic external event risk assessments aswell as assessments of safety margins with respect to tsunami.

10

Table 2.2-1 IAEA’s approach to defense in depth and examples of design standard positioning(Atomic Energy Society of Japan, 2014)

Figure 2.2-1 Key elements of the integrated risk informed decision making process (IAEA, 2011;
Narumiya, 2014)11

2.3 Tsunami Sources for Assessment
2.3.1 Tsunami Causal Factors
As presented in Section 2.1 of the main volume, when considering the safety of nuclear power
plants in the future, many natural phenomena will be subject to consideration. With respect to tsunami
as well, we need to take account of the fact that it is not just fault motions but other factors that also
cause tsunami. In addition, as necessary, multiple factors should be considered as necessary forassessment selection, which are anticipated to have a significant impact on the site of a nuclear power
plant. The factors causing tsunami which are regarded as subject to assessment are given below.
[Fault motions]・ Earthquakes along plate boundary
・ Inland crustal earthquakes[Non-fault motions]・ Submarine landslides
・ Slope failures
・ Volcanic phenomena (sector collapse, caldera collapse, etc.)
2.3.2 Combinations of Causal Factors
Taking into account the relationship between causal factors and the geological context of the areasurrounding a site that is related to tsunami causal factors, consideration is given to earthquakes alongplate boundary and as other earthquakes as well as combinations of earthquakes and submarine
landslides or slope failures on the premise that there is a cause-and-effect relationship. Volcanic
phenomena (sector collapse, caldera collapse, etc.) are understood to be independent events andmainly regarded not as being subject to combination.
2.4 Tsunami Action for Assessment
The water rise and water fall due to tsunami is subject to assessment. Moreover, as necessary,
fluid force, sediment transport, flotsam and other actions resulting from tsunami at a site or in the areasurrounding a site are subject to assessment.
In order to put in place a design so that important facilities are not impaired from the perspectiveof the impact of a tsunami on a nuclear power plant, it is important to assess the maximum water risefor the purpose of assessing any inundation of the site accompanying the water rise, and the maximum
water fall to assess the impact on important safety functions involved in water intake capability or the12amount of time affecting water intake. Moreover, from the perspective of defense in depth, it isnecessary to consider the impact on important facilities that actions resulting from a tsunami otherthan water level change have when considering the design of a nuclear power plant. Typical actions
attributable to a tsunami are given below.
・ Inundation, flood damage and submersion due to a rise in the water level・ Water fall affecting water intake
・ Generation of fluid force (tsunami pressure, tsunami force, buoyancy force, etc.)
・ Topography change due to sediment transport (erosion, sedimentation, and scouring)・ Generation, floating and collision of flotsam
2.5 Composition of this Publication
Figure 2.5-1 presents an overview of tsunami assessment and a flowchart showing therelationship of the chapters of the main volume. First, the necessary surveys (Chapter 3) are conducted
and detailed assessments are then conducted. The assessment methods employed at such time may beclassified into two types: Deterministic tsunami hazard analysis and Probabilistic tsunami hazard
analysis.
・ Deterministic tsunami hazard analysis (DTHA): For the target nuclear power plant, a tsunami
source is configured that takes into account the necessary uncertainty, and action in the areasurrounding the plant due to a tsunami generated by this source is computed using numericalsimulation and other methods.
・ Probabilistic tsunami hazard analysis (PTHA): For the target nuclear power plant, multiple
tsunami causal factors are selected that are thought to have a certain impact on the target nuclear
power plant, and the probability of a tsunami occurring is computed in relation to the tsunami
water level, taking into account any necessary uncertainty.
Generally speaking, DTHA is mainly considered for assessments of tsunami water level in thedesign of outdoor facilities and soundness assessments. On the other hand, PTHA results may be linked
to Probabilistic Tsunami Fragility Analysis (PTFA) and accident sequence analysis, thereby making it
possible to compute core damage frequency and other tsunami risks (Tsunami PRA*).
Core damage frequency is one index showing the safety of a nuclear power plant when
considering measures for quantitatively reducing tsunami risk.
*PRA: Probabilistic Risk Assessment
As with the IRIDM approach described in Section 2.2 of the main volume, DTHA, Tsunami PRA
and other methods may be appropriately combined to assess risks attributable to tsunami as well aschanges in risks resulting from countermeasures to determine more appropriate proposals for13

countermeasures. In this publication, Chapter 4 and 5 respectively describe DTHA and PTHA withrespect to Tsunami PRA. Also, assessments of the action of inundation, tsunami force and otherproperties attributable to tsunami necessary for assessing such tsunami risks are described in Chapter
6.
An appendix volume have been compiled to supplement this main volume. The appendix volume
is a compilation of tsunami propagation calculations as well as specific methods for assessing tsunami
force, seafloor topography change, flotsam collision force and so on as well as seismological andgeophysical knowledge that may be utilized for configuring fault models. There are also case studies
showing the application of DTHA and PTHA.

Figure 2.5-1 Overview of nuclear safety assessments with respect to tsunami and relationship ofchapters

14

2.6 Definition of Terms
The definitions of terms used in this volume are given below.
・ Examination-subject tsunami
Of the tsunami that might arise in the future in the seas around Japan including sea areas along
the Japan Trench, Kuril Trench, Nankai Trough, eastern margin of the Japan Sea as well as off
the coast of Chile or other distant places, tsunamis for which it is appropriate to consider that
their impact on the site under examination will be maximum are defined as “examination-subject
tsunami”.
・ Examination-subject tsunami group
Users may conduct parametric studies using examination-subject tsunamis for the site to be
examined. We define a set of those tsunamis as “examination-subject tsunami group”.
・ Probable maximum tsunami
From an examination-subject tsunami group, a tsunami for which the maximum water rise or
maximum water fall (for time affecting water intake depending upon power station conditions)
at assessment points will be maximum is defined as a “probable maximum tsunami”.
・ Parametric study
With respect to examination-subject tsunami caused by standard fault model defined withseismological parameters, investigating such parameter sensisivities onto examination-subject
tsunami, within reasonable parameter ranges, using a set of numerical simulations is defined as a"parametric study". Such parametric study leads us to estimate how the uncertainty in tsunami
causal factors affects a probable maximum tsunami.
・ Standard fault model
A fault model for a parametric study is defined as a "standard fault model".
・ Maximum water level ascent and maximum water level descent
These terms are defined as follows.
・Maximum water level ascent: The maximum rise in water level measured from the suitable
tidal level on which numerical simulation is carried out (Positive value)・Maximum water level descent: The maximum fall in water level measured from the(suitable) tidal level on which numerical simulation is carried out (Negative value)15

[Chapter 2 References]
Atomic Energy Society of Japan’s Investigation Committee on the Nuclear Accident at the Fukushima
Daiichi Nuclear Power Plant (2014): Full Picture of the Fukushima Daiichi Nuclear Power
Station Accident and Proposals for Tomorrow: Final Report of the Society’s Accident
Investigation, 448p.
Committee on Specific Topics Concerning Civil Engineering Technology for Nuclear Safety (2013):
Proposal on Optimal Earthquake and Tsunami Resistant Performance of Nuclear Power Plants(Civil Engineering Perspective).
http://committees.jsce.or.jp/2011quake/node/158 (Accessed on April 2016)
IAEA (2011): A Framework for an Integrated Risk Informed Decision Making Process (INSAG-25),
The International Nuclear Safety Group, 23p.
http://www-pub.iaea.org/MTCD/publications/PDF/Pub1499_web.pdf (Accessed on April
2016)
Japan Association for Earthquake Engineering (2014): Tsunami Resistant Engineering for Nuclear
Safety: Aiming for a Comprehensive System of Technology for Tsunami and Earthquake
Defense, 283p.
Joint Editorial Committee for the Reports on the Great East Japan Earthquake Disaster (2013): Reporton the Great East Japan Earthquake Disaster: Mechanical Engineering Volume, 93p.
Kameda, H. (2011): Earthquake Engineering Issues Pertaining to the Safety of Nuclear Power Plants,
Bulletin of the Japan Association for Earthquake Engineering, No. 15, Special Issue on the
Great East Japan Earthquake, pp. 97-102.
Narumiya, Y. (2014): Issues Concerning the Decision-Making Process for Safety Improvement
Measures, Atomic Energy Society of Japan 2014 Fall Meeting, 13p.
http://www.aesj.or.jp/comittees/gijiroku/etc/sc2014f-0301.pdf(Accessed on April 2016)
Nuclear Regulation Authority (2013a): New Regulatory Requirements for Commercial Power
Reactors, Nuclear Fuel Facilities, etc.
http://www.nsr.go.jp/activity/regulation/tekigousei/shin_kisei_kijyun.html (Accessed on April
2016)
Nuclear Regulation Authority (2013b): Operation Guide for Safety Improvement Assessments ofCommercial Power Reactors, Nuclear Fuel Facilities, p. 37.
http://www.nsr.go.jp/data/000085457.pdf (Accessed on April 2016)
Yamaguchi, A. (2012): Current Status and Future Expectation concerning Probabilistic Risk
Assessment of Nuclear Power Plants, Journal of the Atomic Energy Society of Japan, Vol. 54,
pp. 184-190.
16

Chapter 3 Investigations Necessary for Tsunami Assessment
There are a broad variety of factors that cause tsunami including earthquakes along plateboundary, fault motions resulting from inland crustal earthquakes or other such seismic movements in
sea areas as well as natural phenomena other than fault motions including submarine landslides, slope
failures, volcanic phenomena (flank collapse, caldera collapse, etc.). Accordingly, for tsunami
assessments, it is necessary to conduct appropriate investigations that take into account the relationshipbetween tsunami causal factors and the geographic characteristics of the assessment points.
The investigations necessary for tsunami assessment are explained in detail with fiveclassifications broadly divided in accordance to the objective: investigations of past tsunami,
investigations of tsunami propagation routes, investigations concerning the configuration of tsunami
source models, investigations of sediment transport due to tsunami, and investigations of tsunami
debris.
3.1 Investigations of Past Tsunami
3.1.1 Literature Survey
In order to identify past tsunami that may have had a significant impact on an assessment point,
a literature survey is conducted of historical records that include evidences of past tsunami, tsunami
deposit and oral traditions as well as records of earthquakes that have occurred and other data. The
following sorts of publications may be part of a literature survey of past tsunami.
・ Watanabe, Hideo (1998): Comprehensive Survey of Destructive Tsunami in Japan (Second
Edition), University of Tokyo Press.
・ National Astronomical Observatory, Editor: Chronological Scientific Tables, Maruzen.
・ Usami, Tatsuo et al. (2013): Comprehensive Survey of Destructive Earthquakes in Japan 5992012, University of Tokyo Press.
・ Utsu, Tokuji (1982): Table of M6.0 or Greater Earthquakes and Destructive Earthquakes Near
Japan: 1885 to 1980, Bulletin of the Earthquake Research Institute of The University of Tokyo,
Vol. 57, pp. 401-463.
・ Utsu, Tokuji et al., editors (2001): Encyclopedia of Earthquakes (Second Edition), Table ofMajor Earthquakes in Japan, Asakura Publishing Co., Ltd., pp. 569-641.
・ Shuto, Nobuo et al., editors (2007): Encyclopedia of Tsunami, Appendix Table, Asakura
Publishing Co., Ltd., pp. 333-341.
・ Abe, Katsuyuki (1988): Quantification of Earthquake and Tsunami near Japan According toTsunami Magnitude, Bulletin of the Earthquake Research Institute of The University of Tokyo,
17

Vol. 63, pp.289-303.
・ Abe, Katsuyuki (1999): Determination of Tsunami Magnitude Mt Using Run-up Height,
Earthquake Second Compendium, Vol. 52, pp. 369-377.
・ Tsunami Deposit Database: https://gbank.gsj.jp/tsunami_deposit_db/
・ Trace of past tsunami Database: http://tsunami-db.irides.tohoku.ac.jp/
・ Investigative reports by universities and other research institutions as well as the Japan
Meteorological Agency and other public agencies
・ Scholarly publications by researchers (series of research publications on historical tsunami by
Hatori and other scholarly publications)
In cases where far-field tsunami are examined, it is conceivable that there may be effects
attributable to tsunami mainly following earthquakes that are estimated to occur near plate boundaries
off the coast of Chile or the Cascadia region, so data on past tsunami and other information is alsocollected with respect to such tsunami sources.
Of the various records concerning evidences of past tsunami, the height of traces evidencing
tsunami prior to the 1896 Meiji Sanriku earthquake-tsunami have been projected by researchers basedon ancient documents and other literature sources as well as oral traditions and other legends, so thereliability of tsunami height traces is closely scrutinized as necessary. With respect to the height ofrelatively newer traces identified since that time, the methods for investigating tsunami trace height aswell as their reliability in individual references are scrupulously examined, and, in cases wherereliability is suspected, it is desirable to return to the encyclopedia or other source to conduct a precise
review and critically study the pros and cons of adopting such data in assessments.
With respect to past tsunami that have occurred in recent years, there are cases where water levels
and waveforms have been observed, so, from tide observation data provided by the Japan
Meteorological Agency and other sources with respect to tide levels (high and low water levels, etc.)
at assessment points, records from the automatic the tide gauge stations may be utilized.
3.1.2 Tsunami Deposit Investigations
In order to obtain information other than from literature surveys of ancient documents and othersuch sources about the run-up height record of past tsunami, tsunami deposit investigation are
conducted as needed.
A tsunami deposit investigation surveys records based on literature surveys and topographicalsurveys of ancient earthquakes and tsunami that are assumed to have had an impact on the site, terrain
where it appears that tsunami deposit may remain, information concerning sources supplying deposit,
as well as changes and other alterations to the paleoenvironment. Next, taking into account the results
18

of literature and topographical surveys, fieldwork is conducted to check for any possibility thattsunami deposit may be remaining as well as examine the sedimentation environment so as to evaluate
the effectiveness of on-site surveys.
In the on-site surveys, in order to acquire information about whether or not tsunami deposit ispresent, the frequency with which tsunami occur, their scale and other such data, exploratory drillingand other such means are employed to collect samples of sediment going back to the Jomon
Transgression. With respect to the samples of event sediments obtained through exploratory drillingor other such means, in keeping with the characteristics of the survey points and the condition of thesediment, sedimentological analyses, chronological analyses, paleontological analyses and other suchanalyses are appropriately combined to analyze and study sedimentary structure, sediment thickness,particle size distribution, distribution elevation and planar sediment distribution, presence of oceanic
origins substances, changes in the sediment environment, simultaneity with crustal movements, andother characteristics, and these are contrasted with historical records as well as the results of surveys
conducted by various institutions to identify and confirm the tsunami deposit.
The “Guide for Surveying and Assessing Tsunami Deposit” (Japan Nuclear Energy Safety
Organization, 2014a) and “Tsunami Deposit Handbook” (Japan Nuclear Energy Safety Organization,
2014b) serve as references for the methods for surveying and assessing tsunami deposit.
3.2 Investigations of Tsunami Propagation Routes
Topographic surveys are conducted in sea and land areas in order to gain an understanding of
topographical features and propagation routes from the tsunami source related to the tsunami
assessment up to the area around the assessment point (taking into consideration land run-up). As forthe currently available material related to topography of marine areas, topographic data concerning
the seas around Japan that may be referenced include:
・Japan Hydrographic Association: JTOPO30
・Japan Hydrographic Association: Bathymetric digital data (M7000 and M5000 series)
・Japan Hydrographic Association: Bathymetric and geological survey reports
・Japan Coast Guard: Basic maps of the sea along the coast
・Japan Coast Guard: Basic maps of the sea along the continental shelf・Japan Coast Guard: Various nautical charts
・Japan Coast Guard: J-EGG500・National Institute of Advanced Industrial Science and Technology: Various marine geologicalchartsMaterial that may serve as references for areas around assessment points includes:
・Coastal administrative authorities: Depth measurement data
19

・Port administrative authorities: Top views of ports
・Fishing port administrative authorities: Top views of fishing ports
・River administrative authorities: Results of river longitudinal and cross-section measurements
In addition, in cases where the analysis region is extremely broad, topographic data that covers theentire earth may also be used, such as:・National Geophysical Data Center (NGDC): ETOPO1, ETOPO2 (Global Relief Model)
・International Hydrographic Organization (IHO)
・Intergovernmental Oceanographic Commission of UNESCO (IOC): GEBCO (General
Bathymetric Chart of the Oceans)
On the other hand, as for currently available material pertaining to typography of land areas, thebasic map data published by the Geographical Survey Institute (digital elevation models, 5m grid, 10m
grid) as well as elevation data measured with aerial lasers, which has been carried out by local
governments and companies, and basic urban planning maps prepared by local governments as wellas other such data may be used.
When performing numerical simulation for past tsunami and assess tsunami deposit surveys, incases where artificial modifications (structures, etc.), which did not exist when the tsunami struck
previously, are reflected in the latest topographical data and cases where there is the likelihood thatthe impact or other effects of fault motions have significantly altered the topography or elevation
around an assessment point, consideration is given to reconstructing past topographical data prior tothe modification using ancient maps or other sources as necessary and then utilizing the reconstructed
data.
3.3 Investigations on Configuration of Tsunami Source Models
3.3.1 Literature survey
In the configuration of tsunami source models due to earthquakes occurring along plateboundaries, users may utilize information about the earthquakes that are considered to have had an
impact on the site in the past, and may collect knowledge about source mechanisms of large eathquakes
not only in Japan but also the world as well as their tectonic setting. In particular, with respect totsunami generated by earthquakes along plate boundary, it is important to utilize knowledge abouttsunami generated by great earthquakes that occurred in the world in the past, including the 2011
Tohoku earthquake.
In the configuration of tsunami source models for tsunami that originated from inland crustal
earthquakes offshore around the site, ones may collect information from previous literature and othersources about location, geometry, activity, length (between edges), etc. of active faults, and, as
20

necessary, ones may obtain records of acoustic(seismic) explorations from the Japan Coast Guard,
National Institute of Advanced Industrial Science and Technology (NIAIST), Geological Survey ofJapan and other such institutions, and then may reanalyze them to re-interpret acoustic profiles.
Ones may take into account reports prepared by earthquake model review committees andworking groups which have been established by institutions such as the Central Disaster Prevention
Council, Cabinet Office, and Ministry of Land, Infrastructure, Transport and Tourism, as references
for basic information about the configuration of tsunami source models for tsunami attributable tolarge-scale fault motions.
In addition to referencing assessments of earthquakes and tsunami as well as long-term
assessments of active faults and subduction-zone earthquakes by the Headquarters for Earthquake
Research Promotion, a framework for seismotectonic divisions, which is presented in the assessment
methods for earthquakes whose hypocenter parameters is difficult to identify in advance, may also bereferenced for the probabilistic assessments described in Chapter 5.
In the assessment of tsunami generated from submarine landslides, slope failures, volcanic
phenomena (flank collapse, caldera collapse, etc.), it is necessary to configure the tsunami source
model appropriately, by reffering current knowledge and surveys by businesses. Previous case studiesof tsunami generated from such non-seismic events are mentioned in Section 4.6.4 of the appendix
volume.
With respect to the distribution of submarine landslides, ones may reference traces of submarine
landslides are indicated on submarine geological maps, made by the NIAIST/ Geological Survey ofJapan. With respect to the distribution of slope failures and other such phenomena on land, ones may
reference landslide topographical distribution maps

and earthquake hazard stations (including

landslide topographical distribution map databases) published by the National Research Institute for
Earth Science and Disaster Resilience. In addition, with respect to volcanic phenomena, the NIAIST
has publicly released a database of active volcanoes, and the Japan Meteorological Agency has
released information on the distribution of active volcanoes in Japan. Ones may utilize these sources.
There are also cases where tsunami at the assessment point or in the surrounding area have beenassessed by government institutions, in addition to tsunami source models that have been proposed inscientific literature by researchers. In the configuration of tsunami source models, ones may collectsuch information about the approach adopted for tsunami source model configuration as well as
analysis conditions and others, and may utilize these information as necessary.
3.3.2 Offshore surveys
In the assessment of tsunami originating from crustal earthquakes, ones may conduct surveys inoffshore around the power plant area, as necessary, to investigate submarine topography, geologic
21

stratigraphy, stratigraphic distribution, geological structures and other such features for the purpose ofclarifying the location, geometry, activity, length (between edges) and other characteristics of active
faults.
There are cases where it is useful to conduct offshore surveys to estimate the location, size, andranges of collapse and sedimentation with past submarine landslides.
3.3.3 Collection and Analysis of Other Information and Knowledge
There are seismic observations, crustal movement observations and other such observations
which have been conducted by businesses. Ones may utilize the observation data.
3.4 Investigations of Sediment Transport Caused by Tsunami
In assessing the impact that sediment transport caused by tsunami have on water intake at a power
plant, the distribution and characteristics of bottom sediment are ascertained by means of on-site
surveys and other such investigations of sea areas in front of assessment points as well as by means ofliterature surveys for the purpose of obtaining parameters to be used in the calculation of sedimenttransport employing models for forecasting topography change.
In cases where it has been determined that bottom sediment is comprised of sand and otherdeposits that tsunamis have likely swirled up, samples are taken to obtain data on particle size
distribution, specific gravity and other properties.
In the literature available on bottom sediment, there are, for example, bottom sediment (surface
deposits) distribution maps, basic maps of the sea (Japan Coast Guard), and data detailing sedimentthat has been collected. In addition, the methods employed in field surveys of bottom sediment include
boring and side-scan sonar.
3.5 Investigations of Tsunami debris
In assessing the soundness of tsunami protection facilities and other such structures, objects are
anticipated that may become tsunami debris and their physical quantities are estimated for the purposeof assessing such impact following collision of tsunami debris with a facility.
Objects that may become tsunami debris include fishing boats and other vessels navigating theareas around the power station, some of the structures installed in the tsunami run-up area around a
power plant, various types of wood and lumber, as well as structures, vehicles and other such objects
in the area where flooding is anticipated at a site. From among these, objects that may conceivably
have an impact on power station facilities due to collisions are identified, and the physical quantities
22

estimated as necessary for calculating the size, weight, specific gravity and other such data necessary
for calculating the impact force of debris.

[Chapter 3 References]
Japan Nuclear Energy Safety Organization (2014a): Guide for Surveying and Assessing Tsunami
Deposits.
Japan Nuclear Energy Safety Organization (2014b): Tsunami Deposits Handbook.
National Research Institute for Earth Science and Disaster Resilience: Landslide Topographical
Distribution Map.
http://dil-opac.bosai.go.jp/publication/nied_tech_note/(Accessed on August 2016).
National Research Institute for Earth Science and Disaster Resilience: Seismic Hazard Stations.
http://www.j-shis.bosai.go.jp/map/ (Accessed on August 2016)23

Chapter 4 Deterministic Tsunami Hazard Analysis
4.1 Basic Matters
4.1.1 Flowchart of Deterministic Tsunami Hazard Analysis

The basic flow of a deterministic tsunami hazard analysis is shown in Figure 4.1.1-1.
Investigation for tsunami
assessment

Chapter 3 of the main Volume

Selection of tsunami causal factors
Sections 4.1.2 - 4.2.2

Source modelling of probabletsunamiConsideration of uncertainties

Sections 4.1.3 and 4.2.3

Selection of probable maximum
tsunamiSection 4.3

Figure 4.1.1-1. Basic flow of a deterministic tsunami hazard analysis
4.1.2 Selection of Tsunami Causal Factors
Of those tsunamis that have possibility to occur in the future, the tsunamis that are appropriately
regarded as being likely to have the greatest impact on the site are set as probable tsunami. Also, theaggregate of probable tsunamis is referred to as a probable tsunami group.
In the selection of tsunami causal factors, of those tsunami causal factors listed in Section 2.3 ofthe main volume as well as such combinations, multiple causal factors are selected that are believed
to have a significant impact on the site on the basis of survey results. In so doing, there are simplified
prediction techniques, which are given below, that serve as methods for selecting causal factors witha significant impact.
・

tsunami by fault motion: Abe (1989), etc.

・tsunami by slope failure: Huber and Hager (1997) (see Section 4.2.2 of the the main volume)24

4.1.3 Consideration of Uncertainties
The uncertainties of the tsunami sources are taken into account in the assessment of tsunami
impact on a site.
For tsunami attributable to fault motion, it is conceivable that a parametric study of fault
parameters (described in Section 4.2.3.1 of the main volume) may be conducted using the standard
fault model as well as the possibility examined of multiple seismically-active areas being active
simultaneously.
For tsunami for which the primary cause is not fault movement, case studies are taken into
account that indicate the possibility of a tsunami amplifying due to submarine landslides or
earthquakes such as the 1998 Papua New Guinea earthquake (Japan Society of Civil Engineers, 2002)
to also examine the likelihood that fault motion and tsunami attributable to other factors may occur
almost simultaneously, and, in cases where there is the possibility of simultaneous occurrence, areview is conducted also of the superposition of such events. The following cases are examples ofsuch occurrences.
・Superposition of tsunami resulting from submarine landslide and resulting from fault
motion・Superposition of tsunami resulting from slope failure and tsunami resulting from fault
motionThe focus is on the maximum water level ascent and descent (time affecting water intake
dependent upon power station conditions), and, as necessary, an examination may also be conductedof wave period, impact on geomorphic change, etc.
4.2 Preparation of Probable Tsunami
4.2.1 Fault Motion-Caused Tsunami
4.2.1.1 Basic Policy for Configuration of Tsunami Source for Probable Tsunami Caused by Fault
Motion(1) Earthquake Occurrence Patterns
The patterns of earthquake occurrence that may turn into factors causing a tsunami are taken
into account in configuring the default fault parameters for the wave source of a probable tsunami.
The following is a list of examples of patterns of earthquake occurrence that may turn into
factors causing a tsunami around Japan.

251) Earthquake along the plate boundaries
1-1) Inter-plate earthquake resulting from plate subduction
1-1-a) Archetypical inter-plate reverse fault earthquake
1-1-b) Tsunami earthquake1-2) Intraplae earthquake within a subducting plate
1-2-a) Normal fault earthquake
1-2-b) Reverse fault earthquake2) Inland crustal earthquake2-1) Earthquake along the eastern margin of the Japan Sea
2-2) Earthquake due to a submarine active fault
And, as necessary, combinations of the aforementioned 1) and 2) may also be taken into
account.
In the majority of coastal regions, a near-field tsunami will be used as the target for the wave
source of a probable tsunami, but, in some cases, it is conceivable that a far-field tsunami may
have a greater impact on the assessment points. For this reason, as necessary, the impact is also
added, which results from a tsunami occurring off the coast of Chile or the Cascadia region orother far-field tsunami have, in configuring the wave source of a probable tsunami.
(2) Location and Scale
The occurrence region and scale of the earthquake are appropriately configured taking into
account current stress conditions and other factors, which are based on the crustal structure,
distribution of active faults, state of asperities, conditions in which past earthquakes occurred,and other such data.
(3) Configuration of Fault ParameterIn the configuration of fault parameter for the wave source of a probable tsunami, a scaling
law may be applied that is appropriate in keeping with the crustal structure, characteristics of thesea area, patterns of earthquake occurrence that give rise to tsunami, and other factors.
Three approaches are shown below with respect to scaling laws for fault parameters that are
relevant to moment magnitude.
1) Method that does not set a limit for fault length L, fault width W or average slip amount D2) Method setting a limit only for fault width W
3) Method setting a limit for average slip amount D and fault width W
With respect to inter-plate earthquakes, a typical example of numeral 1) is the relational
26

expression described by Murotani et al. (2013) that yields a relationship among seismic moment,
fault area and average slip for earthquakes having a moment magnitude up to 9. Other
representative scaling laws are shown in Sections 2.1.2 and 2.4.1 of the appendix volume.
(4) Heterogeneity of Slip
In cases where heterogeneous slip may be configured for the fault plane on the basis ofknowledge about slip distribution and calculations reproducing past tsunami, it is desirable totake such facts into account.
In cases where heterogeneous slip is taken into account, the slip amount, area and position
may be configured for a large slip region using inversion calculations for past tsunami as well as
knowledge about inter-plate earthquakes, which is available from the Cabinet Office (2012),
Japan Nuclear Energy Safety Organization (2014), and other references.
4.2.1.2 Configuration of Tsunami Source Caused by Earthquakes along Plate Boundary(1) Assessment Objects
On the basis of knowledge about plate tectonics in the area surrounding Japan,
characteristics of earthquakes that have occurred and characteristics of fault models rendering
these, the area around Japan is believed to be divided into the two types of sea areas indicatedbelow. For this reason, assessments are conducted of tsunami originating in earthquakes alongplate boundary included within these sea areas.
・Sea area associated with subduction of the Pacific Plate

・

Sea area associated with subduction of the Philippine Sea Plate
Moreover, in addition to the aforementioned sea areas, as indicated in Section 4.2.1.1 of themain volume, as necessary, the assessment may also cover far-field tsunami occurring off thecoast of Chile, Cascadia region or other such areas.
(2) Standard Fault Model
Taking into account the location and pattern of earthquake occurrence, a fault model that isin keeping with the moment magnitude and other characteristics of anticipated tsunami isconfigured as the standard fault model.
Examples of methods for configuration of standard fault models for each sea area are shownin Section 2.2.5 of the appendix volume. In addition, details about the basis for configuration ofstandard fault model for specific sea area and other such particulars are given in Sections 2.2.1
through 2.2.4 of the appendix volume.
In the sea area along the Japan Trench and Kuril Trench (southern part) as well as the sea
27area along the Nankai Trough, tsunamis have repeatedly occurred in the past, and there is arelative wealth of knowledge about plate boundary profiles and other such characteristics, so suchknowledge may also be utilized in configuring a standard fault model that reflects thedistinguishing features of each sea area. Modeling is carried out with consideration given to
information about the profile of plate boundaries and motion direction. However, as necessary,faults near the trench axis on the Pacific side which are believed to be bifurcated from the plateboundary surface are subject to modeling, taking into account the impact and other characteristics
on tsunami that occur as well as the activity of target faults.
When assessing probable tsunami in sea areas other than the aforementioned, a standard
fault model is configured based on scaling laws and other knowledge of tsunami accompanying
earthquakes near plate boundaries as well as the profile of plate boundaries.
(3) Tsunami Source Location
The location of the standard fault model is set in keeping with the pattern of tsunami
occurring at locations considered to be reasonable, taking into account the conditions in whichpast earthquakes have occurred and other seismological knowledge and information. In addition,with respect to the division of regions for wave source configuration, divisions are appropriately
configured based on crustal structure, pattern of earthquake occurrence and other data. However,as necessary, an examination is also conducted of the possibility that the region near a trench axis
and the zone for a typical interplate thrust earthquake may be active at the same time, taking into
account knowledge acquired about the 2011 Tohoku earthquake.
4.2.1.3 Configuration of Tsunami Source Caused by an Earthquake Anticipated near the EasternMargin of the Japan Sea(1) Assessment Objects
With respect to the eastern margin of the Japan Sea, it is believed that a mature plateboundary surface has not formed, but from the area off the western part of Hokkaido extending
to the area off the western part of Niigata Prefecture, there are regions where strain has
concentrated due to crustal movements (strain concentration zones), and, in the surrounding areas,large earthquakes and tsunami caused by such have almost continually occurred in a spatial
manner. Taking into account to this fact, separate from assessments of tsunami following
earthquakes anticipated in sea-area active faults, tsunamis following earthquakes for which it isappropriate to assume might occur along the eastern margin of the Japan Sea are regarded as
subject to assessment.

28

(2) Standard Fault Model
Taking into account the location and pattern of earthquake occurrence, a fault model that isin keeping with the moment magnitude and fault length of anticipated tsunami is configured as
the standard fault model. Methods and other information about configuring standard fault models
for the eastern margin of the Japan Sea are given in Section 2.3.2 of the appendix volume. Also,
details about the basis for configuration of standard fault models and other such particulars are
given in Section 2.3.1 of the appendix volume.
Along the eastern margin of the Japan Sea, because it is believed that a mature plateboundary surface has not formed, uncertainty about the parameters including the dip angle isreflected as derived from the fact that earthquakes have occurred having different dip directions,and limitations on the thickness of the seismogenic layer are taken into account in applying thescaling law indicated in Section 2.4.1 of the appendix volume.
(3) Tsunami Source Location
The location for the standard fault model is set in keeping with the pattern of tsunami
occurring at locations considered to be reasonable, taking into account the conditions in whichpast earthquakes have occurred and other seismological knowledge and information. The
standard fault model may take into account knowledge about the conditions in which pastearthquake have occurred, strain concentration zones and other data to work out a configurationin keeping with the pattern of tsunami occurrence at a location which is considered reasonable
and has been divided up in more detail.
4.2.1.4 Configuration of Tsunami Source Caused by an Earthquake in Submarine Active Fault(1) Assessment Object
Although there are not known cases of large-scale damage due to a tsunami originating from
activity in a submarine active fault, tsunami resulting from earthquakes anticipated in submarine
active faults where there is a possibility of activity in the future are subject to assessment.
The tsunamis following an earthquake anticipated in a submarine active fault, which are
addressed here, are different from those pertaining to the sea area division indicated in Section
4.2.1.2 (1) and 4.2.1.3 (1) of the main volume, as they refer to the entire sea area around Japan.
Simplified prediction techniques are utilized to compare approximate estimations oftsunami height at assessment points, thereby making it possible to identify tsunami to be subject
to detailed assessment from among multiple active faults. The method using the Mt equation byAbe (1989) and other such methods serve as simplified prediction techniques for identifying whatshould be subject to assessment. However, assessments using simplified prediction techniques
29are rough estimations based on a statistical relationship found among earthquake magnitude,
propagation distance and tsunami height, and the impact of water depth at the tsunami source
location and the coastal topography are not directly taken into account. For this reason, in cases
where the results of a narrowing down of objects to be assessed using simplified prediction
techniques provides multiple tsunami resulting from earthquakes anticipated in submarine active
faults considered to have a significant impact at the assessment points, it is desirable to performa detailed assessment employing numerical simulations with respect to these.
(2) Standard Fault Model
Taking into account the characteristics of individual submarine active faults, a standard fault
model is configured in keeping with such characteristics. Configuration methods are given in
Section 2.4.2 of the appendix volume. Also, specific details about the basis for configuration of
the standard fault model and other particulars are given in Section 2.4.1 of the appendix volume.
With respect to tsunami originating from earthquakes anticipated in submarine active faults,
limitations on the thickness of the seismogenic layer are taken into account in configuring thestandard fault model by applying a scaling law similar to that for the eastern margin of the Japan
Sea reflecting uncertainty about parameters, including dip angle.
(3) Fault Location, etc.
The fault location, fault length and strike direction of submarine active faults are configured
based on literature surveys, surveys of submarine active faults for individual assessment points
and other data. Similarly, with respect to inclination angle and other parameters as well, cases
where it is clear, based on literature surveys, surveys of submarine active faults for individual
assessment points and other data, that the dip angle and other such parameters may also be treatedin a definite manner similar to fault length and strike direction.
It is also possible to configure the slip angle of a fault based on the relationship of wide-area
stress field and fault plane angles as well as other data (see Section 2.4.3 of the appendix volume).
4.2.2 Non-Fault Motion-Caused Tsunami
4.2.2.1 Basic Policy for Preparation of Probable Tsunami Not Caused by Fault Motion
There are tsunamis that occur due to submarine landslides, slope failures or volcanic phenomena(flank collapse, caldera collapse, etc.) that cause move of ocean water. In cases where such topography
or traces are observable, tsunami that are believed to have an impact on a site may be subject toassessment based on information about such scale and location of occurrence obtained from surveys.
30

Past examples comprising such phenomena include the tsunami that originated from the 1741
Oshima-Oshima flank collapse.
4.2.2.2 Selection of Tsunami Source(1) Examination Objects
Based on the scale of the phenomenon, positional relationship with the site and other factors
as well as simplified prediction techniques, it is possible to identify targets for detailed assessment
from multiple assessment objects. For example, the following formula is given, which has been
derived from tests employing hydraulic models using slope failure in Huber and Hager (1997) asa simplified formula relating to water level during the initial period of a tsunami resulting fromslope failure.
1/ 4  r
H
 2 
 2  0.88 sin  cos2  M 1 / 2  s   d 3  w   d 

2 / 3M  Vs bd 2

where, H: Total tsunami amplitude, d: Water depth at the slide location, α: Inclination of the slip
plane, γ: Incident angle, ρs: Slide density, ρw: Seawater density, r: Propagation distance, Vs: Slide
volume, and b: Slide width.
In identifying the objects to be assessed, slope inclination, landslide scale, water depth andother data necessary using simplified prediction techniques are appropriately configured basedon surveys.
(2) Tsunami Source Location, etc.
In accordance with the results of investigations as described in Chapter 3 of the main volume,
location and scale are configured, and the tsunami source that is thought to have a significant
impact on the site is selected.
It is generally known that tsunami following a submarine landslide, slope failure or volcanic
phenomenon (flank collapse, etc.) has high directionality of energy in the incident direction
compared to a tsunami originating in a fault motion. For this reason, after appropriately
configuring the location and other characteristics for the tsunami source based on surveys, therelationship of the tsunami source’s position with the site is taken into account in selecting atsunami source that is regarded as having a significant impact.

31

4.2.3 Consideration of Uncertainties
4.2.3.1 Uncertainty Related to Tsunami Caused by Fault Motion
Conducting a parametric study of a standard fault model is one method of considering uncertainty.
In a parametric study, numerical calculations are conducted by modifying parameters for importantfactors within the parameters of a standard fault model where uncertainty is present (location, length,
width, strike direction, dip angle, slip amount, slip angle, slip distribution, upper edge depth, failure
initiation point, failure propagation velocity, etc.) to assess a probable tsunami group. In assessing aprobable tsunami group, it is important that the factors used to conduct the parametric study beappropriately selected, and their scope reasonably prescribed.
As for other uncertainties, it is also conceivable that multiple seismically-active areas may be
active simultaneously, as discussed in Section 4.1.3 of the main volume. In this section, the basic
approach to parametric study will be addressed.
(1) Parametric Study Procedures
Of the parameters of the standard fault model, after a parametric study is conducted of thosefactors regarded as relatively more dominant, it is fundamental that a fault model be used thatsets parameters having the greatest impact on the site from among such factors so as to conduct
a perimeter study of other subordinate factors.
Parametric study are carried out on each water level rise and fall.
(2) Parametric study Factors
In principle, a standard fault model is utilized to conduct a parametric study of factors
determined to have relatively significant uncertainty. In so doing, consideration is given towhether or not tsunami source uncertainty is expressed by any of the parameters. Typical factors
are given in Section 3.1 of the appendix volume.
Moreover, with respect to inter-plate earthquakes for which the expansion of the tsunami
source is very broad, consideration is also given to dynamic parameters (failure propagation
velocity, failure initiation point, etc.) which represent chronological change of the fault motion
in keeping with the extent of the impact.
(3) Scope of Parametric study
With respect to the scope of the parametric study, the scope for modifying the parameters
regarded as reasonable is appropriately configured by taking into account the degree of
uncertainty. In addition, with respect to factors that may be statistically processed based on data32

about past earthquakes, the extent of the standard deviation may serve as a yardstick for the scope.
With respect to the tsunami sources of tsunami resulting from earthquakes anticipated along
the eastern margin of the Japan Sea or submarine active faults, the scope is indicated in thestandard fault model with regard to factors considered to have relatively large uncertainty (seeSection 3.2 of the appendix volume). In such a case, a parametric study may be conducted using
such scope as the standard.
4.2.3.2 Other Uncertainties(1) Consideration of Combinations of Tsunami Causal Factors
In cases where tsunami, which are caused by multiple factors that have a cause-and-effectrelationship, occur almost simultaneously, the superposition of these is taken into consideration.
For example, in a case where the possibility is recognized that a both a tsunami resulting fromfault motion and a tsunami resulting from a submarine landslide may occur, the phenomenon isassessed in which both are superimposed. In so doing, in cases where the locations where theanticipated tsunami are to occur are away from each other as well as cases where a tsunami having
a small scale is included, the tsunami to be superimposed are selected after reviewing thepossibility that superposition may have a significant impact on the site.
(2) Consideration of Time Differences
From the perspective of impact on the site, differences in the time when tsunami resulting
from various factors occur are taken into consideration. For example, in a case where seismic
ground motion induces a submarine landslide, time differences may be taken into consideration
within such scope when the difference in time is able to be configured within a reasonable scope,such as taking into consideration the duration over which seismic ground motion, whose theprimary factor is a submarine landslide, continues.
4.3 Selection of Probable Maximum Tsunami(1) Selection of Probable Maximum Tsunami
Of the probable tsunamis, those for which the maximum water level ascent or descent (timeaffecting water intake dependent upon power station conditions) at the assessment points is thegreatest are selected as probable maximum tsunami. In so doing, it is fundamental that the meanhigh tide level is taken into account for water level rise, and the mean low tide level for waterlevel fall. Moreover, in cases where vertical displacement of the site is anticipated accompanying
fault motion, it is necessary to select the probable tsunami for which the relative amount of the33

water level change is the maximum in relation to the site level.
(2) Necessary Conditions
With respect to probable maximum tsunami it is to be verified that at least one of thefollowing conditions “(A)” or “both (B-1) and (B-2)” is satisfied. However, the “vicinity of theassessment point” is appropriately configured after studying similarities between the coastal andsubmarine topography and the assessment points, number and distribution of the heights of traces
evidencing past tsunami which are regarded as having a significant impact on the assessment
points.
(A)

There is evidence of the height of past tsunami regarded as having a significant impact
on the assessment point, and the results of calculations of probable maximum tsunami
exceed such heights.

(B-1)

The results of calculations of probable maximum tsunami exceed the results ofcalculations of past tsunami at the assessment point.

(B-2)

The envelope curve of the results of calculations of the probable tsunami group exceeds
tracing evidencing of the height of past tsunami in the vicinity of the assessment points.

The intent is to have the conditions set for (A), (B-1) and (B-2) confirm that the rise in waterlevel of a probable maximum tsunami selected after estimating for a variety of types of
uncertainty exceeds the evidence of the height of traces of past tsunami at least at the assessment
points. Accordingly, in cases where there is evidence of the height of past tsunami believed tohave a significant impact on an assessment point, it is sufficient to verify only (A). In cases where
there are no records of traces of past tsunami at an assessment point, then it is desirable to satisfy
both (B-1) and (B-2), but if there are limits on the amount of information that may be acquired
about the evidence of the height of past tsunami, then it is sufficient that either (B-1) or (B-2) beverified. In so doing, past tsunami of a small-scale for which it is clearly evident that the level
was below the scenario tsunami at the assessment point may be omitted from confirmation.
Although probable maximum tsunami does not need to have an occurrence profile orlocation that is identical to past tsunami for which records of such traces have been produced,
attention does need to be given to the fact that satisfying “(A)” or “both (B-1) and (B-2)” is theminimum requirement for a determination probable maximum tsunami. In addition, in cases
where tsunami deposits are able to provide information about the range of tsunami inundation, it
is desirable to closely examine the reliability of tsunami deposits in obtaining the results ofcalculations for inundation that comprise these distribution ranges.

34

[Chapter 4 References]Abe, Katsuyuki (1989): Estimate of tsunami heights from magnitudes of earthquake and tsunami,
Bulletin of the Earthquake Research Institute, The University of Tokyo, Vol. 64, pp. 51-69 (inJapanese with English abstract).
Cabinet Office Study Group on Models for Massive Earthquakes in the Nankai Trough (2012): Study
Group on Models for Massive Earthquakes in the Nankai Trough (Second Report) Tsunami
Fault Model Volume: Tsunami Fault Models and Tsunami Height, Inundation, etc. (inJapanese).
http://www.bousai.go.jp/jishin/nankai/model/pdf/20120829_2nd_report01.pdf (Accessed on
August 2016)
Huber, A. and W. H. Hager (1997): Forecasting impulse waves in reservoirs, in Dix-neuvieme Congres
des Grands Barrages, Florence, Commission Internationale des Grands Barrages, pp. 993-1005.
Japan Nuclear Energy Safety Organization (2014): Guidelines for Developing Design Basis Tsunami
Based on Probabilistic Approach, JNES-RE-Report Series, JNES-RE-2013-2041, 193p.
Japan Society of Civil Engineers Nuclear Civil Engineering Committee (2002): Tsunami Assessment
Method for Nuclear Power Plants in Japan.
Murotani, S., K. Satake and Y. Fujii (2013): Scaling relations of seismic moment, rupture area, average
slip, and asperity size for M~9 subduction-zone earthquakes, Geophysical Research Letters,Vol. 40, pp. 1-5.

35Chapter 5 Probabilistic Tsunami Hazard Analysis
5.1 Overview of Probabilistic Tsunami Hazard Analysis
5.1.1 Basic Flow of Probabilistic Tsunami Hazard Analysis
Probabilistic tsunami hazard analysis is a method for obtaining the relationship between tsunami
height and the exceedance probability during a specific period of time, and current methods forprobabilistic tsunami hazard analysis have been proposed for such references (Annaka et al., 2006;
Annaka et al., 2007; Geist and Parsons, 2006; Sugino et al., 2008; Japan Society of Civil Engineers,
2011; Japan Nuclear Energy Safety Organization, 2014; etc.).
The purpose of probabilistic tsunami hazard analyses, which are premised on the presence of
uncertainty, is to systematically process a variety of types of uncertainty related to estimation so as tofind the relationship between tsunami height and the exceedance probability during a specific periodof time and thereby provide data for making an engineering determination. Important differences fromthe deterministic method are that probabilistic tsunami hazard analyses reflect all conceivable eventsin the assessment and specifically take into account time (occurrence frequency).
In the assessment, a logic tree is configured that takes into account uncertainty upon the basis ofpast earthquake data and other factors for the region around a nuclear power plant to compute theexceedance (occurrence frequency) probability of the tsunami water level, which is likely to attack in
the future. The basic flow of probabilistic tsunami hazard analysis is shown in Figure 5.1.1-1.
With a probabilistic hazard analysis of the earthquake and tsunami, one must be mindful that, incases where a change occurs in the understanding of earthquakes and tsunami, the configured logic
tree also changes.
Collection and analysis of relevant
data

Section 5.1.4

Configuration of logic tree

Section 5.2

Probabilistic tsunami hazard
analysis

Section 5.3

Figure 5.1.1-1 Basic flow of probabilistic tsunami hazard analysis
5.1.2 Two Types of Uncertainty and Logic Tree Approach
A probabilistic tsunami hazard analysis is premised on the presence of uncertainty and provides
36

data for making an engineering decision under such conditions. This uncertainty is generally divided
into two types for consideration: aleatory uncertainty and epistemic uncertainty.
Aleatory uncertainty is uncertainty that is attributable to randomness inherent in a physicalphenomenon and is regarded as unpredictable. In a probabilistic tsunami hazard analysis, aleatory
uncertainty is taken into account within one tsunami hazard curve.
Epistemic uncertainty is uncertainty that is attributable to insufficient knowledge or awareness,such as the problem of whether or not there is an active faults or the range of magnitude that mightoccur, a solution to the problem may be finalized if research is advanced, but, currently, the issue isunpredictable, and it is taken into consideration as branches of logic tree and expressed by multiple
tsunami hazard curves.
To take into account epistemic uncertainty is to create a tsunami hazard curve group with weights
based on multiple combinations corresponding to epistemic uncertainty. The logic tree approach is amethod for systematically conducting this, and the results are mainly expressed as a fractile. A fractile
hazard curve (percentile hazard curve) indicates the level of equal non-exceedance probability for aset of hazard curves. An illustration of a logic tree is shown in Figure 5.1.2-1.
The logic tree approach is generally utilized in probabilistic hazard analysis of earthquakes andtsunami in order to quantitatively reflect in assessments the likelihood of each opinion at the current
point in time with respect to individual issues where there are multiple opinions, even among experts.
Accordingly, in this publication, descriptions are provided on the assumption that the logic tree
approach is utilized. However, if there are other methods where epistemic uncertainty is able to betreated quantitatively, then such methods may serve as an alternative for the logic tree approach.

Earthquake
occurrence model

Tsunami occurrence
model

Probabilistic
process

Occurrence
location

Occurrence
interval

Earthquake
scale

A1 1 

B1 1 

C1  1 

D1  1 

E1 1 

F1  1 

A 2  2 

B2  2 

C2  2 

D2  2 

E2  2 

F2  2 

B3  3 αi, βj , γkOccurrence
patternD 3  3 

and other such symbols indicate the weight of each branch component.
Figure 5.1.2-1 Illustration of a logic tree
37

Variance oftsunami estimatesF3  3 

5.1.3 Assessment Objects
In this publication, the object of probabilistic tsunami hazard analyses is tsunami for which thedirect cause is a fault motion. The reflection of tsunami arising due to submarine landslides, slope
failures, volcanic phenomena (flank collapse, caldera collapse, etc.) and other factors that are not fault
motion is regarded as an issue to be pursued in future research. However, if there are objects for which
the scope of uncertainty relating to the occurrence frequency, scale or occurrence pattern is able to beappropriately configured, then it is also possible to reflect such in the assessment.
The probabilistic tsunami hazard analysis is a method for obtaining the long-term average hazard
and the hazards during a particular period of time beginning at the current point in time. The former
assesses the long-term average annual exceedance probability. The latter assesses the exceedance
probability during a specific period of time beginning from the point in time subject to assessment.
Information about the earthquake occurrence probability (frequency) found in the former forms thefoundation for assessment of the latter. In the former assessment, as part of the earthquake occurrence
probability, data about the average activity interval (occurrence frequency) is used to obtain theearthquake occurrence probability by means of a stationary process (ex. Poisson process). On the other
hand, in the latter assessment, data about the time of the most recent occurrence (last event) in addition
to the average recurrence interval is used to assess the exceedance probability during a specific periodof time by means of a renewal process (ex. BPT (Brownian Passage Time) distribution).
5.1.4 Collection and Analysis of Relevant Information
Information is collected about the occurrence pattern of earthquakes which give rise to tsunamithat may impact a power plant (active fault data, data about past earthquakes, etc.). The collection of
information from experts is also effective for expressing epistemic uncertainty in branches of logic
tree.
When the latest knowledge or other such information has been announced that may have a verysignificant impact on a probabilistic tsunami hazard analysis, such a data needs to be appropriatelyreflected.
5.2 Basic Approach to ModelingThis chapter shows in detail the modeling of earthquakes necessary for probabilistic tsunami
hazard analyses apply to nuclear power plants, which are described in Section 5.3 of the main volume,
procedures for assessment of tsunami height distribution, and the methods of setting up branches and38

weights on logic trees for a tsunami assessment.
5.2.1 Modeling of Earthquakes of which Source Parameters can be Expected Seismologically
The components that must be modeled for earthquakes of which source parameters can be
expected seismologically are listed below.
・What is the region over which earthquakes occur? (Occurrence region)・What magnitude earthquakes occur at what rate? (Magnitude distribution)

・What is the frequency at which earthquakes occur? (Average recurrence interval anduncertainty)

It is sufficient that the aforementioned three components be configured in cases where one typeof earthquake occurs within one region of activity. But, in cases where there are multiple segments
and where rupture of single segment connected rupture of multiple segments or other such situations
are intermingled, the following components are taken into account in modeling.
・

What frequency does each segment rupture?

・What kind of combination of segments will be ruptured simultaneously?

・What are the respective frequencies that combinations of segments, which rupture
simultaneously, occur?

・What kind of magnitude of earthquakes occur at what rate for each combination ofsegments that ruptures simultaneously?

(1) Source Region
The identification of source regions for earthquakes that may occur in the future on the basisof past earthquakes has generally been undertaken for regions where earthquakes have occurredin the past. However, although these are tectonically similar environment, the identification of
the appropriate region is not easy in cases where there are regions where earthquakes haveoccurred and regions where they have not. Such an example may be seen in the case of tsunami
earthquakes and normal fault earthquakes along the Japan Trench. Addressing this kind of issue
using a logic tree is regarded as effective.
With tsunami earthquakes and normal fault earthquakes along the Japan Trench as well as
earthquakes along the eastern margin of the Japan Sea and other such seismic events, it is argued
whether the regions where earthquakes occur are completely separate (there is no fault across theregion) or continuous. Addressing this kind of issue also using a logic tree is regarded as effective.
In addition, the source region of a submarine active fault may be configured based onliterature surveys and surveys of submarine active faults relating to individual assessment points.

39

(2) Magnitude Distribution
The distribution width of the magnitude of characteristic earthquakes is considered because,
in reality, the characteristic earthquake magnitude is believed not to be limited to one value andto have a significant impact on tsunami.
The magnitude range of past characteristic earthquakes where it is believed that almost thesame region ruptured are shown in Table 5.2.1-1. The magnitude width is distributed across a
range from 0.3 to 0.5, so 0.3 and 0.5 are set as the magnitude distribution width.
In order to determine the magnitude distribution width, the specific MW which is basis forthe scenario of each sea region (hereinafter referred to in this section as “Mc (central magnitude)”),is required to be assumed, and the position of Mc in the MW distribution have to be defined. In sodoing, Mc is determined by taking into account the characteristics of each sea region (crustal
structure, distribution of active faults, state of asperities, conditions in which past earthquakes
occurred, etc.). The possibilities that Mc may take with respect to the distribution width are shownin Figure 5.2.1-1. There is a possibility of eight patterns in all and it is difficult to make a definite
determination, so addressing this situation using a logic tree is regarded as effective. In such acase, if Mc is appropriately expected taking into account the characteristics of each sea region,
then it is considered sufficient for Mc to omit the three patterns near the lower limit of the
distribution width and consider the five patterns shown in Figure 5.2.1-1. Also, for inter-plate
earthquakes, seismic moment may also be computed based on stress drop and the active region
area. In such a case, the results of examining the stress drop of inter-plate earthquakes around theworld can be used. The results of the investigation conducted by the Cabinet Office (2012) cameup with an average value of 1.2MPa as shown in Figure 5.2.1-2, and, according to the scaling law
provided by Murotani et al. (2013), the mean value is 1.6MPa (see Section 2.1.2 of the appendix
volume). In cases where +1σ is taken into account as the variance 2.2MPa was obtained in the
study by the Cabinet Office (2012) and 3.0MPa by Murotani et al. (2013). Based on the
aforementioned results, stress drop may also be considered on branches of logic tree.
(3) Average Recurrence Interval and Uncertainty
The average recurrence interval is required in hazard analyses of long-term averages (timeindependent hazard analysis) as well as instantaneous (time dependent hazard analysis) hazard
analyses, but variance is required only for instantaneous hazard analyses.
1) Logarithmic Normal Distribution and Brownian Passage Time (BPT) Distribution
The recurrence interval for characteristic earthquakes is modeled using the logarithmic
normal distribution or Brownian Passage Time (BPT) distribution.
BPT distribution is a model that takes into account a physical process (Brownian relaxation40

oscillator process) where “in the stationary process of stress accumulation due to plate motion,
the stress accumulation reaches a certain threshold and the fault becomes active (earthquake
occurs) within a context where disturbance of the stress field is added which is expressed as
Brownian motion, which includes the occurrence of an earthquake and a slow event near thetargeted hypocentral region”, and is expressed using the following formula (Ellsworth et al.,
1999; Matthews et al., 2002).

Y t     t    W t 
where, Y(t) is the state variable, and t is the elapsed time since the last time it reached Yf, and,
when Y(t) reaches Yf, then an earthquake occurs and a state is fallen into Y0. λt is a term derived
from stationary stress accumulation, and δW(t) is a term derived from disturbance of the stressfield. W(t) is standard Brownian motion, and δ is a nonnegative constant, and δ2 is referred toas a diffusion coefficient.
The distribution function for time t that elapsed from the time when Yf was last reached(since the earthquake occurred) until Yf is reached next (an earthquake occurs) is called the
BPT distribution. The density function of the distribution is given using the following formula.

 

f t ;  ,     2 2 t 3

 exp  t    2  t 
1

2

2

2

The mean of this distribution is μ, and the variance is (μα)2. Also there is the following
relationship with λ and δ.

  Y f  Y0     Y f  Y0   2
1

Variance  Y f  Y0  2 3
The BPT distribution is also called the inverse Gaussian distribution or Wald distribution
in the field of statistics, and has been applied to stock price fluctuations, product life, etc.
An overview of the BPT distribution has been given above, and, in practice, there is no
significant difference between the BPT distribution and logarithmic normal distribution. An
example is given in Figure 5.2.1-3.
In a case where there are n units of data regarding the recurrence interval of characteristic
earthquakes, the m (median value) of the logarithmic normal distribution is:

1nTi
n
i 1
n

m

and the μ (mean value) of the BPT distribution is:Tii 1 nn Both are calculated using the arithmetic mean. The logarithmic standard deviation σln41expresses variance across the average recurrence interval in a logarithmic normal distribution,and α in the BPT distribution, and the logarithmic standard deviation σln is calculated using:n1nTi  m2

i 1

n

1n  and α in the BPT distribution is calculated using:
1 Ti
1
n
i 1
n

 2  An example of an assessment conducted in the Headquarters for Earthquake Research
Promotion (2001) is shown in Table 5.2.1-2. Although σln is slightly smaller, both values arealmost equal. Based on this table, the variance value is at the level of 0.2 to 0.4.
2) Error in Average Recurrence Interval of Characteristic Earthquakes
In cases where the average recurrence interval of a characteristic earthquake is based ondata, it is natural to set branches of logic tree that are based upon error.
If the true value of the distribution mean is x and the arithmetic mean xo, then the meanvalue of xo-x is zero and the standard deviation (standard error for the distribution of true valuex) is:

n
σ is the standard deviation of x. Because the number of data about the average recurrence
interval is small, if the value previously described is used as the standard deviation, then the
degree of reliability (error) of the estimated value corresponding to the amount of data may beassessed.
3) Error in Cases of Poisson Process
Even in cases where the average recurrence interval is given as a Poisson process, it ispossible to assess the confidence interval on the basis of an assessment of standard deviation
determined by the number of data. The variance of Poisson variables will be equivalent to theaverage occurrence frequency when the occurrence frequency is large, and the confidence
interval for occurrence frequency X is expressed as:X X
Error in cases where X is small is given by Weichert (1980). This is shown in Figure 5.2.1-4
and Table 5.2.1-3.
(4) Modeling of Multi-segment Rupture
The combinations of multi-segments in earthquakes that have previously occurred along the42Nankai Trough have changed. Such a phenomenon has also been observed in earthquakes that
occurred off the coast of Miyagi Prefecture as well as those that have occurred off the coast of
Tokachi and Nemuro. As for the earthquakes off the coast of Miyagi Prefecture, cases have beenreported where land-side earthquakes and earthquakes along trenches have occurred multisegment rupture as well as cases where these earthquakes have occurred separately. In addition,with respect to the Japan Trench extending from off the coast of Sanriku to off the coast of Boso,
2011 Tohoku tsunami had a source region comprising the area near the Japan Trench in off thecoast of southern Sanriku, part of the region near the Japan trench extending from off the coastof northern Sanriku to off the coast of Boso, off the coast of central Sanriku, off the coast of
Miyagi Prefecture, off the coast of Fukushima Prefecture, off the coast of Ibaraki Prefecture andother such regions, and this occurrence region is currently still being studied (The Headquarters
for Earthquake Research Promotion, 2011). As for the area off the coast of Tokachi and Nemuro,it has been estimated that earthquakes have occurred in which segments off the coast of Tokachi
and off the coast of Nemuro have multi-segment rupture at an interval of around 400 to 500 years(ratio of about once in 6 times) (Central Disaster Prevention Council, 2006). With respect toinland active faults as well, based on the different times when activity has occurred in the past in
the main part of the Nobi fault zone, it has been estimated that activity has taken place in three
separate segments, the Neodani fault zone, Umehara fault zone and Mitahora fault zone, but it
has also been said that it is likely that entire main region of the fault zone was active as one
activity segment in a more ancient activity (The Headquarters for Earthquake Research
Promotion, 2005).
A schematic depiction of this phenomenon is shown in Figure 5.2.1-5. Such a model is calleda cascade model (series model) in the study by the Working Group on California Earthquake
Probabilities (“WGCEP”) (1995) and a multi-segment model in the study by Odagiri and
Shimazaki (2000).
When a historical record of multiple earthquakes that have occurred over a relatively long
period of time is available, it is considered feasible to estimate the long-term multi-segment
probability based upon actual past events (multi-segment rate), and the following kinds ofmethods are conceivable in cases where a pattern of multi-segment is anticipated for which themulti-segment rate is not clear or occurrences in the past have not been confirmed.
[1] Estimation from the multi-segment rate obtained in adjacent sea areas or sea areas that are
geo scientifically similar.
[2] A multi-segment earthquake is considered as an independent characteristic earthquake, andthe recurrence interval is set independently based upon estimated slip and strain
accumulation rate (back slip).
[3] The Gutenberg-Richter formula (G-R law; Gutenberg and Richter, 1944), which is applied for43

a region, is utilized to extrapolate the frequency of multi-segment earthquakes based upon
the frequency of activity of each segment.
Of the aforementioned, [3] is the method that the Headquarters for Earthquake Research
Promotion (2014) applied to active faults in Kyushu.
It is conceivable that there are many cases where sufficient information is unable to beobtained to uniquely determine all multi-segment patterns. In such a case, it is desirable to reflectmultiple combinations in branches of logic tree.
Currently, in hazard analyses, one issue for future study is to find a method for how toestimate the probability of occurrence for each combination. As the rupture probability for eachsegment is able to be found based on the average rupture interval and variance of each segment
as well as the time of the most recent occurrence, a method is required for converting this into
the probability of each segment combination occurring.
With respect to a case where an earthquake off the coast of Tokachi and an earthquake off
the coast of Nemuro occurred in a multi-segment manner, the Headquarters for Earthquake
Research Promotion (2014) used a method where: The probability of the earthquakes occurring multi-segment during the target period
is estimated.
 The obtained probability is multiplied by the rate of multi-segment, which is basedon actual earthquakes that have occurred in the past and other such data.
WGCEP (1995) presented a method where: In the case of multi-segment earthquakes, half of the past occurrence frequency is
assumed;-If an earthquake occurs n times over a period of T years, then 0.5n/T is assumed;
 In the case of single segment earthquake, half of the expected occurrence value isassumed.
 So that the number of earthquakes is the minimum, the remaining number is allocatedwith priority given to large earthquakes.
Annaka et al. (2001) presented a method that partially revises WGCEP (1995) where: In the case of multi-segment earthquakes, half of the past occurrence frequency is
assumed;-If an earthquake occurs n times over a period of T years, then 0.5n/T is assumed;
 In the case of single segment earthquake, a value is assumed that is found by
multiplying the probability at which ruptured in single segment in the past against the
expected occurrence value.
 So that the number of earthquakes is the minimum, the remaining portion is allocatedwith priority given to large earthquakes.
44

Examples of assessments conducted by Annaka et al. (2001) of the average occurrence
frequency for each combination of Boso offshore, the inside of Sagami Bay and West Sagami
Bay fractures are shown in Table 5.2.1-4.
Shimazaki et al. (1998) presented an approach that yields constraint conditions. In contrast
to determining an allocation so that the aforementioned method satisfies the rupture probability
for each segment, the rupture probability of each segment is not always satisfied when specificconstraint conditions are given as was done in Shimazaki et al. (1998).
Besides the multi-segment probability, there is the scaling relationship-related issue of how
to determine the magnitude for multi-segment earthquakes.
In cases where the slip of each segment is not so dependent on multi-segment, it is possible
to add together seismic moments with regard to moment magnitude, so it is regarded as feasible
to set the moment magnitude for each segment and add that together, thereby setting the moment
magnitude for multi-segment earthquakes.
In cases where the slip of each segment changes significantly due to multi-segment, the rangeof the moment magnitude requires to be set separately from each segment.
(5) Application of the G-R Model to Megathrust Earthquakes Occurring along Plate Boundaries
With respect to megathrust earthquakes occurring along plate boundaries, there is a method
based on the characteristic earthquake model, and a method based on the G-R model that calculates
the magnitude and frequency of earthquakes occurring in regional source based on probability andstatistics, and these may be regarded as branches of logic tree taking into account epistemic
uncertainty. Illustrations of both are shown in Figure 5.2.1-6. Of the graphs shown in Figure 5.2.16, (a) shows a G-R model, and (b) shows the relationship between magnitude and the number ofearthquakes in one earthquake cycle which includes maximum magnitude Mmax. In addition, thenumber of earthquakes at each magnitude is expressed by n, and the cumulative number ofearthquakes based on those having a greater magnitude is expressed by N. Although the G-R modelshows a sequential distribution up to maximum magnitude, the characteristic earthquake model
does not have any earthquakes between maximum magnitude Mmax and the second greatest
earthquake magnitude Ma.
In cases where the G-R model is used, it is necessary to model the magnitude distribution inadvance. Illustrations of the logic trees for the G-R model and characteristic earthquake model are
shown in Figure 5.2.1-7. Specific details of the investigation are given in Section 7.1.1 of theappendix volume.

45

Table 5.2.1-1 Range of magnitude of past characteristic earthquakes
Sea region

Range of MJ

Miyagi Prefecture offshore: 5 earthquakes

7.3 ~ 7.5

Northern Sanriku offshore: 4 earthquakes

7.4 ~ 7.9

Tokachi offshore: 2003, 1952, 1843

8.0 ~ 8.2

Nankai Trough: 1946, 1854

8.0 ~ 8.4

46

Probability
density
確率密度

Mc

(a)
1/5
Probability
density
確率密度-0.2 -0.1(b)+0.1 +0.2

Mw

1/3
Probability
density
確率密度-0.1

Probability
density
確率密度-0.3 -0.2 -0.1

Mw

+0.1

(c)
1/5

(d)

+0.1

Mw

1/3

Mw

-0.2 -0.1

Probability
density
確率密度

(e)
1/5

Mw

-0.4 -0.3 -0.2 -0.1
Probability
density
確率密度

(f)
1/5
Probability
density
確率密度

-0.1

(g)

+0.1 +0.2 +0.3

Mw

1/3

Mw

+0.1 +0.2

Probability
density
確率密度

Mcが保守的でPattern that may be
あれば除外でexcluded if Mc is
きると考えられ
conservative
るパターン

(h)
1/5
+0.1 +0.2 +0.3 +0.4

Mw

Figure 5.2.1-1 Possiblity of position of Mc to distribution width of magnitude

47

Eathquake

2003 Tokachi-oki

Referencedata

MO(N m)

S(km2)Mw

σ(MPa) log10(Δσ) Earthquake- Earthquake- Residual Variance Residual
specific
for eachfor each
specific
median mean value earthquake earthquake
MPa
value

Tanioka et al. (2004)

Tu

1.00E+21

8

9600

2.6

0.41

Satake (1993)

Tu, G

3.90E+21

8.3

59400

0.7

-0.15

0.41

2.60

0.00

0.000

0.108

0.006

0.018

0.004

0.095

0.01

Kato and Ando (1997)

Tu, G

4.00E+21

8.3

54000

0.8

-0.10

Tanioka and Satake(2001a)Baba et al. (2002)

Tu

5.30E+21

8.4

52650

1.1

0.04

Tu

4.90E+21

8.4

52650

1

0.00

0.00

Satake (1993)

Tu, G

2.00E+21

8.1

48600

0.5

-0.30

0.01

Kato and Ando (1997)

Tu, G

2.80E+21

8.2

43200

0.8

-0.10

Tu

2.00E+21

8.1

42525

0.6

-0.22

2011 Tohoku
Earthquake2010 Chili
earthquake

Tanioka and Satake(2001b)Cabinet Office

4.21E+22

9.0 1.20E+05

2.5

0.39

0.39

2.47

0.00

0.000

0.093

1.55E+228.8130000

0.8

-0.08

-0.08

0.83

0.00

0.000

0.029

2004 Sumatra
earthquake

Lorito et al. (2010)

Tsunami+GPS
GPS+Tsunami+InSAR
GPS+Tsunami+Satellite

6.63E+229.153150000.9-0.03

Fujii and Satake

Tsunami+Satellite

6.00E+229.12220000

1.5

0.16

0.07

1.17

0.009

0.000

1946 Nankai

1944 Tonankai

Lorito et al. (2011)

-0.05

-0.22

0.89

0.60

0.00
0.01

0.02
0.00

0.01
0.01

Mean of the median

Variancelog(Δσ)

0.09

0.069

Δσ

12

Standard deviation
0.26+Standard deviation

22- Standard deviation

0.7

Figure 5.2.1-2 Consolidation of mean stress drop based on analysis using tsunami

Logarithmic
normalProbability density

Probability of earthquake not occurring

observation data (Cabinet Office, 2012)

Elapsed time (years)

Logarithmic
normalElapsed time (years)(BPT: μ=157.8,α=0.367, Logarithmic normal:m=4.996,σ=0.358)
Figure 5.2.1-3 Examples of comparison of BPT distribution and logarithmic normal distribution

48

Table 5.2.1-2 Examples of assessments of variance(The Headquarters for Earthquake Research Promotion, 2001)
Region assessedσlnαNankai

0.358

0.367

Miyagi Prefecture offshore

0.176

0.177

Atera

0.287

0.293

Tanna

0.211

0.213

Atotsu River

0.164

0.165

Western edge of Nagano basin

0.247

0.250

Figure 5.2.1-4 Confidence intervals for Poisson variables (Weichert, 1980)

49

Table 5.2.1-3 Confidence intervals for Poisson mean (Weichert, 1980)

50

Time

Successive
occurrence

SingleInduced

Rupture cycle 2
Multi-segment rupture

Multi-segment

Rupture cycle 1
SingleDisplacement

Activity history

Unit displacement distribution

Geometric segment

Rupture segment

Fault model

Figure 5.2.1-5 Conceptual diagram of multi-segment model (cascade model) (Sugiyama, 1998)

51

Table 5.2.1-4 Examples of occurrence frequency in multi-segment model (Annaka et al., 2001)
Method 1 (WGCEP method)

Method 2 (Revised WGCEP method)

Segment

A Bosooffshore

B SagamiBay

C West Sagami
Bay fracture

A Bosooffshore

B SagamiBay

C West Sagami
Bay fracture

Rupturefrequency

0.80

4.54

13.70

0.8

4.54

13.70

Single rupture

0.00

2.27

11.43

0.00

0.00

9.16

A+B

-

0.00
-

B+C
A+B+C

-

0.00
-

1.47
0.80

3.74
0.80

* Figures indicate the number of earthquakes per 1,000 years

Figure 5.2.1-6 G-R model and characteristic earthquake model (Wesnousky, 1994)

52

Earthquake magnitude distribution
model

Occurrence frequency andmaximum Mw

b valueb value1

P1 (Mw)
Mwmax1G-R modelb value2

P2 (Mw)
Mwmax2

Characteristic
earthquake model

Figure 5.2.1-7 Illustration of logic trees for G-R model and characteristic earthquake model
5.2.2 Modeling of Background Earthquakes
Background earthquakes (earthquakes other than earthquakes of which source parameters can be
expected seismologically) are regarded as being sequentially distributed along plate boundaries, within
the crust or other regions, so segmentation of active regions and the magnitude frequency distributionof each activity region are required. The basic process for such configuration is shown below.
(1) Segmentation of Active Regions
A segmentation of active regions should be zoned for each target point, and the segmentation
may be referenced for assessing earthquakes for which it is difficult to specify in advance theearthquake source fault in the segments given in the models proposed by the Headquarters for
Earthquake Research Promotion (e.g. Headquarters for Earthquake Research Promotion, 2014).
(2) Model of Magnitude Frequency Distribution
When the segmentation of active regions are set, the magnitude frequency distribution foreach active region is required. The principal methods currently used are the following two.
The first is the truncated Gutenberg-Richter (G-R) law, which truncates the regular G-R law
at the maximum magnitude Mmax. The equation is given as:
log n = a – bM

(M ≤ Mmax)

where n is the number of earthquakes having magnitude M (density, interval frequency).
The other is the modified G-R law (Utsu, 1971). The equation is given as:
log n = a – bM + log(Mc – M)
where Mc is the maximum magnitude.

53

As shown in Figure 5.2.2-1, in an actual frequency distribution, it is known that the greater
M becomes, the lower the curve bends, and the frequency with which large magnitude
earthquakes occur decreases compare to the linear relationship with the G-R law. The modified
G-R law revises this by having the curved line not exceed the maximum magnitude.
(3) Assessment of Magnitude Frequency Distribution
If a model is determined that is applicable to magnitude frequency distribution, then what
remains is to determine the parameters based on data and to appropriately assess error.
1) Exclusion of Non-Independent Earthquakes
Based on earthquake data, it is necessary to exclude earthquakes that are not independent(aftershocks, foreshocks, and earthquakes except for those that are the maximum size inearthquake swarms).
Although simplified methods have been proposed for excluding such non-independent
earthquakes (Ministry of Construction’s Public Works Research Institute, 1983; Annaka et al.,2002), individual determinations may be made.
2) Assessment of Magnitude Frequency Distribution
There are differences in the range of magnitude of earthquakes, which have been completely
recorded over their duration. It is believed that ordinarily all earthquakes of M6.0 or greater havebeen recorded without omission since 1885, and earthquakes of M5.0 since 1923.
In a case where the truncated G-R law is used, the number of earthquakes (generally, theannual occurrence frequency of those of M5.0 and greater), b values and maximum magnitude
should be set based upon data.
A method for assessing error in the magnitude frequency distribution has not been
established, but one method has been proposed by Annaka and Yashiro (2000), and a method has
been presented where the number of earthquakes of M5.0 or greater is a normal distribution, bvalue a normal distribution, and maximum magnitude is a uniform distribution (or weighted
distribution). In cases where the Monte Carlo method is used, it is possible to generate thenecessary sample from such conditions. It is also possible to have discrete branches.

54

Figure 5.2.2-1 Results of fitting G-R law and modified G-R law to earthquakes worldwide (Mabuchi
et al., 2002)* Dots represent data for the period from January 1977 to December 2001 from the Harvard
University CMT catalog, and the line is the fitted results.
5.2.3 Assessment of Tsunami Height Distribution
In a tsunami hazard curve assessment, the tsunami height distribution has to be estimated for acase where a specific magnitude of earthquake occurs at a specific location. A logic tree for estimatingtsunami height distribution is shown in Figure 5.2.3-1. The background behind each branchcomponents of logic tree is given below.
(1) Setting of Fault Model
A fault model takes into account the characteristics of earthquakes yielding tsunami so as toappropriately create a model of fault motion. Based on a literature survey and other investigation,a fault model is set that is regarded as having an impact on the assessment sites. It is also possible
to set a fault model referencing models proposed by public institutions and others.
Besides historical earthquake data, consideration has to also be paid to traces of liquefaction,
reviews of tsunami deposits and other geological results.
(2) Whether or Not to Consider Parameter Variation
In estimating tsunami height, the fault model, which was set in the aforementioned numeral
55

(1), is used, so it is considered necessary to separately take into account “variation in the fault
model” or to add “variance due to variation in the fault model” in order to consider uncertainty
in the observed and calculated values.
If the model of a fault where earthquakes actually occur varies even in the same location,then the effect attributable to parameter variation is a component that must be taken into
consideration. In the deterministic assessments in Chapter 4 of the main volume, this is regarded
as the “consideration of uncertainty”. Because there is debate about whether or not it is necessary
to take into consideration variances due to variation in fault models in probabilistic assessments,
it is currently regarded as effective to treat the question of whether or not to take into
consideration this variation as a branch.
Even in cases where parameter studies are conducted that take into consideration variationin fault models, just as with the deterministic assessments presented in Section 4.2.3.1 of the main
volume, it is sufficient to assess factors for which it is determined there is relatively great
uncertainty.
(3) Error Standard Deviation and Truncated Range
The uncertainty of estimated values is expressed using either logarithmic normal distribution
or a truncated logarithmic normal distribution, and logarithmic standard deviation (β) andtruncated range (σ) are set as the parameters (specifics concerning the possibility of the varianceof estimated values being approximated with the logarithmic normal distribution are shown in
Section 5.1.1 of the appendix volume).
Logarithmic standard deviation (β) is expressed by the geometric standard deviation
proposed by Aida (1977) (hereinafter referred to in this chapter as “κ”), and the relationship in
between the two is given in the following formula (specifics details pertaining to κ are given in
Section “6.4 Setting of Fault Model Capable of Explaining Run-up Height Record of Past
Tsunami”.).

ln   
where, ln expresses a natural logarithm.
Table 5.2.3-1 shows the results of an examination of κ in relation to past tsunami. In addition,using the results of an examination that took into account 2011 Tohoku tsunami, Sugino et al.
(2014) reported that, in cases where a characterized tsunami source model is used, a logarithmic
standard deviation β=0.2 ~ 0.3 (equivalent to κ=1.22 ~ 1.35) may be assumed under conditions
where the minimum grid size of the area around the site is 5.5m (see Figure 5.2.3-2). On the other
hand, from the results of assessments of wide-area variance using several inversion models of2011 Tohoku tsunami, as shown in Figure 5.2.3-3, results have been obtained where κ=1.3 ~ 1.4,
and both show a variance smaller than that of the results of previous examinations (Table 5.2.356

1).
When using the examination in this publication where the minimum grid size for coastal
areas is set at 50m (Figure 5.2.3-4), all points fall within logarithmic standard deviation (β) of themean of ±4 times. Of these, there were very few results exceeding logarithmic standard deviation(β) of the mean ±3 times, and the effect of local topography, which is unable to be simulated withthe grid size used, is revealed. Specific details of the content considered are given in Section 5.1.2of the appendix volume.
With respect to a truncated range (σ), because it is inconceivable in reality that a value
arrived at by dividing the measured value by the calculated value would infinitely increase, thelogarithmic normal distribution may be truncated using a finite range.
For example, a case where the range is truncated using a mean ±2.3β or a mean ±3β islikened to approximately 1% or approximately 0.1% of one side of the respective logarithmic
normal distribution not emerging. The relationship when this is combined with κ is given as
follows. A case where κ=1.25 ~ 1.55 and the truncated range 3β is the equivalent of likening thattrue values not emerging in excess of 1.253=1.95 to 1.553=3.72 times the results of the numericalsimulation. Or, a case where κ=1.25 ~ 1.35 and the truncated range 3β is the equivalent of likeningthat true values not emerging in excess of 1.253=1.95 to 1.353=2.46 times the results of thenumerical simulation. Details about the truncated range indicated by various institutions areshown in Section 5.1.2 of the appendix volume.
In this way, combinations of logarithmic standard deviation (β) and truncated range (σ) alter
the range of true values estimated based on calculation results, so it is desirable to take into
consideration the complexity of the topography in areas around points subject to assessment, grid
sizes applied, reproducibility of past tsunami and other factors integrated into the branches oflogic tree.
(4) Ergodic Hypothesisκ is an indicator showing the extent to which actual observed values are dispersed in relation
to estimated values at multiple points spread out spatially. The variance used in probabilistic
tsunami hazard analyses expresses the extent to which the tsunami height at specific points basedon the same source (in cases where a specific size earthquake (tsunami) has occurred at a specificlocation) is dispersed temporally in relation to the estimated values.
In probabilistic tsunami hazard analyses and probabilistic seismic hazard analyses, theaforementioned two are ordinarily assumed to be equal (ergodic hypothesis), but there is debate
about the appropriateness of this hypothesis.
Multiple earthquakes along the Nankai Trough have occurred where, although the tsunami
sources have not been the same, tsunami sources have overlapped. The appropriateness of the57

ergodic hypothesis has been examined by studying the correlation of κ at site points of identicalplace name in relation to multiple earthquakes.
The relationship between Ki at site points of identical place name in relation to twoearthquakes where tsunami sources overlap is shown in Figure 5.2.3-5, and relationship between
Ki at site points of identical place name in relation to two earthquakes where tsunami sources do
not overlap is shown in Figure 5.2.3-6. The correlation coefficient (ρ) is shown in each figure.
However, the correlation coefficient is obtained using 1.0 as the mean for K of each earthquake.
From the two figures, it can be seen that the correlation coefficient in relation to the twoearthquakes where tsunami sources overlap displays a greater tendency than the correlation
coefficient in relation to the two earthquakes where tsunami sources do not overlap. Finding themean, the combination of six cases where the tsunami sources overlap is 0.58, and the
combination of four cases where the tsunami sources do not overlap is 0.26. The figure of 0.58
shows that there is a correlation with Ki to a certain extent in the two earthquakes where tsunami
sources overlap.
The fact that there is a correlation with Ki means that the ergodic hypothesis is not completely
correct. In an extreme case, if there were a complete correlation and K were already known inrelation to one earthquake, then the Ki of other earthquake occurring there would be the same,and there would be no variance in relation to Ki.
If Kij in relation to tsunami i and point j is expressed using the mean value and the variance(normal distribution) for the point, then:log K ij   K J   ij
The variance related to log (Kij) (standard deviation) is given as σ, variance related to Kj is given
as σs, and variance related to εij is given as σo, such that: 2   s2   o2And, the correlation coefficient between the two earthquakes is:
 s

2

2

Using a correlation coefficient of 0.58 to calculate the relationship between σo and σ gives:
 o2  0.42 2  0.65 2This indicates that if Kj is known, then the variance will be even smaller than κ estimatedfrom data about past tsunami.
When σ corresponds to κ=1.45, then σo in the above equation corresponds to κ=1.27 as theergodic hypothesis does not hold.
In this assessment, the possibility that the ergodic hypothesis does not hold is given as, κ=1.25
on the branches of logic tree.
58

Location- Horizontal
position- DepthStandard fault
model-Strike-Dip angle-Rake angle-Scaling law-Position and sizeof large slip
region-Deviation in slip
-Rupture strart
point-Rupture
propagation
velocity-Rise time

Relationship between
variation in fault
parameters and estimation
error

Range of variationin fault parameters

Effect of parametervariation is included in κ
(calculation made using
Standard fault model)-Strike-Dip angle-Rake angle-Scaling law-Position and size oflarge slip region-Deviation in slip
-Rupture strart point-Rupture
propagation
velocity-Rise time

Effect of parametervariation is not includedin κ (multiple
calculations are madethat take into accountvariation in fault
parameters in theStandard fault model)

Logarithmic
standard deviationof estimation error

Truncated range oflogarithmic normal
distribution

Logarithmic
standard deviation[1]

Truncated range[1]

Logarithmic
standard deviation[2]

Truncated range[2]

Figure 5.2.3-1 Logic tree for estimation of tsunami height distribution
Table 5.2.3-1(1) κ in cases of uniform slip model*
Sea region

Japan Trench

Nankai TroughEastern margin of
the Japan Sea
Offshore of SouthAmerica

Earthquake-tsunamiκ

Number of run-up heightrecord points compared1933 Showa Sanriku

1.40

572

1896 Meiji Sanriku

1.45

257

1968 Tokachi offshore

1.41

273

1946 Nankai

1.60

159

1944 Eastern Nankai

1.58

43

1854 Ansei Tokai

1.47

89

1854 Ansei Nankai

1.42

60

1707 Hoei

1.35

61

1993 Off the shore of Hokkaido
southwestern coast

1.47

216

1983 Central Japan Sea

1.48

209

1960 Chile

1.37

764

(Median value of the 11 tsunami: 1.453; Median value ± standard deviation: 1.380 ~ 1.529)* Uniform slip on the fault plane is considered.

59

Table 5.2.3-1(2) κ in cases of heterogeneous slip model*
Sea region

Japan Trench

Nankai TroughEarthquake-tsunamiκ

Number of run-up heightrecord points compared

1896 Meiji Sanriku

1.38

143

1611 Keicho Sanriku

1.37

17

1968 Tokachi offshore

1.38

264

1856 Ansei Sanriku

1.45

71

1946 Nankai

1.42

96

1944 Eastern Nankai

1.44

64

1854 Ansei Tokai

1.48

85

1854 Ansei Nankai

1.32

42

1707 Hoei

1.37

49

In (tsunami run-up height record/ calculated tsunami height)* Heterogeneous slip on the fault plane is considered.

Sites in general
Fukushima Daiichi
Fukushima Daini
Onagawa
Tokai Daini

Logarithmic standard deviation
β Characterization

Calculated tsunami height (m)Calculated tsunami height (m)Note: characterized tsunami source model × Minimum grid size 5.5m of topography model

Figure 5.2.3-2 Results of examination of variance assessment using characterized tsunami source
model (Sugino et al., 2014)60

観測値/計算値の幾何標準偏差：κ

Geometric standard deviation of observed
value / calculated value: K

Geometric standard deviation of observed value/calculated value classified by tsunami
waterlevel: K
津波水位別の観測値/計算値幾何標準偏差：κ,
信頼度：A, 距離：500m以内
Reliability: A
Distance: Within 500m

1.45
1.40

CabinetOffice
内閣府
Suginoet al.
杉野ら

1.35

Satakeet al.
SatakeらTakao
et al.
Takaoら

1.30
1.25
1～5

5～10

10～15

15～20

20～

Calculated
water (m)level (m)計算水位

Figure 5.2.3-3 Results of variance assessment using inversion model (Kurita et al., 2013)

Fault model: Cabinet Office model
断層モデル：内閣府モデル／痕跡データ：信頼度Ａのみ(n=2782)
Run-up heightrecord: only reliability A (n=2782)

Observed value/ calculated value
観測値／計算値

10.0

Aza-Ohata, Shomogawa, Izumi-machii,
Iwaki city, Fukushima prefecture

Geometric
mean: 0.956
幾何平均：0.956
Geometric
standard
幾何標準偏差：0.295
deviation: 0.295(κ：1.34)(κ:
1.34)

Ofunato port coast, Ofunato
city

海岸線からの距離：0～100m
Distance
fromcoastline:0-100m
海岸線からの距離：100～200m
Distance
fromcoastline:100-200m
海岸線からの距離：200～500m
Distance
fromcoastline:200-500m

1.0Distance
fromcoastline:500-1000m
海岸線からの距離：500～1000m
±１β
±２β
±３β

Near Miyato Island and Jomon village, Higashi±４βMatsushima city, Miyagi prefecture
Oirase-cho, Kamikita-gun, Aomori prefecture

0.1
34.0

35.0

36.0

37.0

38.0

39.0

Latitude
(°)
緯度（°）

40.0

41.0

42.0

Figure 5.2.3-4 Distribution of observed values/calculated values from results of calculations
reproducing 2011 Tohoku Tsunami61ρ=0.50

K Nankai

K Ansei Nankai

ρ=0.76

K HoeiK Hoeiρ=0.71K Ansei Nankai

K Eastern Nankai

ρ=0.51

K HoeiK Hoeiρ=0.66

K Ansei Nankai

K Ansei Nankai

ρ=0.35

K Nankai

K Eastern Nankai

Figure 5.2.3-5 Relationship of Ki at site points of identical place name in relation to two earthquakes(case where tsunami sources overlap)62ρ=0.31

K Ansei Nankai

K Eastern Nankai

ρ=0.48K NankaiK Nankai

ρ=0.11K Ansei Nankai

K Eastern Nankai

ρ=0.15

K Ansei Nankai

K Ansei Nankai

Figure 5.2.3-6 Relationship of Ki at site points of identical place name in relation to two earthquakes(case where tsunami sources do not overlap)

635.2.4 Method for Classification and Weighting of Logic Tree Branches
The purpose in using a logic tree to conduct a probabilistic tsunami hazard analysis is tosystematically assess uncertainty at the current time with regard to a hazard assessment as well as any
such impact, and to provide information for making an engineering determination under conditions
where uncertainty is existing to that end, it is important that branches of logic tree be built thatappropriately reflect uncertainty at the current time and that the appropriate weight be set for suchbranches of logic tree. However, weighting indicates a determination at the current time about thepossibility of future accuracy, and it is not regarded as being directly related to accuracy in the naturalscience sense.
Components of branches of logic tree are able to be divided into two: “components that are
branches based mainly on differing judgments and should be regarded as discrete branches” and“components that are branches based mainly on error in values estimated from data and should be
regarded as continuous branches”. The former is a component for which a conclusion has been unable
to be reached at the current level that research has reached and includes issues such as how to consider
source regions of normal fault earthquakes and M8 tsunamigenic earthquakes along the Japan Trench.
The latter is essentially determinable based upon data, but is a component for which there are
estimation errors resulting from currently insufficient data and other such factors, and includes theaverage recurrence interval of characteristic earthquakes and other such factors.
Determining the weight of “components that are branches based mainly on differing judgments
and should be regarded as discrete branches” is a “distribution of views of a group of experts at thecurrent time”, and a questionnaire or other such survey is a feasible method of determining weight.
The approach of the Atomic Energy Society of Japan (2012) and other such research may be referenced
with respect to the utilization of “experts”. Such details are given in Section 5.2 of the appendix
volume. Also, setting is possible as shown in Table 5.2.4-1, which is a method of allocating weight incases not based on a questionnaire survey.
With respect to “components that are branches based mainly on error in values estimated fromdata and should be regarded as continuous branches”, it is important to appropriately evaluation error
based on data. As with the method of evaluating error in relation to the average recurrence interval ofcharacteristic earthquakes as indicated in Section 5.2.1 of the main volume, it is necessary that themethod of their evaluation with respect to individual components be clearly defined.
In cases where a continuous distribution is used, it is necessary to utilize the Monte Carlo method
which generates samples using random numbers based on the distribution profile, but it is also
considered possible to use discrete branches instead of a continuous distribution. In this volume, on
the basis of the following approach, the continuous branches (case of normal distribution) have been
replaced with discrete branches.
64

The approach to create branches setting a weight of 0.25:0.50:0.25 in relation to normal
distribution is shown in Figure 5.2.4-1. The normal distribution is divided into three so that the areas
are 0.25, 0.50 and 0.25, and, when the mean weighting of each region is found, it is -1.27σ, 0.0, and+1.27σ. There is also a method where these figures are used directly, but, when consideration is given
to the fact that the accuracy of the estimation of σ is not so high and that it is given approximate
treatment, 1.0 may be used instead of 1.27.

Table 5.2.4-1 Examples of allocation of weighting in cases not based on questionnaire surveys
Weighting allocation(case of two branches)

Prerequisites
Case where a determination on weighting is difficult using
currently available knowledge
Case where weight of one side is regarded as high if based on
relevant data
Case where although the creation of branches is not regarded asnecessary if based on relevant data, consideration is given to thefeasibility of forming this into a branch

0.5 : 0.5
0.3 : 0.7
0.1 : 0.9

0.5

Probability
確率密度density

0.4
0.3

0.5
0.2
0.1

0.25

0.25

0
-3

-2

-1

0

1

2

3

X
*Area weighting means are -1.27, 0.0 and +1.27

Figure 5.2.4-1 Illustration of setting up branches in relation to normal distribution65

5.3 Probabilistic Tsunami Hazard Analysis Procedures
5.3.1 Calculation Procedures
The procedure of the probabilistic tsunami hazard analysis is given below.
(1) Calculation of Earthquake Occurrence Probability
For each seismic region or active fault, the probability of an earthquake occurrence iscalculated. Either of the following methods may be adopted.
For a hazard analysis in the long-term, the annual occurrence frequency of the earthquake
is given. If a Poisson process is assumed, the annual occurrence frequency and annual
probability of exceedance will have a 1:1 correspondence.

For a hazard analysis of the current point, the renewal process is taken into account basedon data about the history of earthquake occurrence and the period of time of most recent
activity to calculate the probability of occurrence during a specific period of time (ex. 50
years) beginning from the current time.

(2) Calculation of Tsunami Height Distribution
Numerical simulations are used to calculate the water level in front of the site for all
scenarios having different calculation configurations. Moreover, error in numerical analysis istaken into account in individual calculation results and converted to a distribution showing theprobability of water level exceedance.
(3) Consideration of Tide Level Distribution
In addition to considering tides as a stochastic process, a distribution is prepared withconditions about the probability of water level exceedance when individual scenarios occur.
(4) Creation of Tsunami Water Level Hazard Curve
The probability of an earthquake occurrence is reflected in the distribution of the probabilityof the water level exceedance in numeral (3) in preparation of multiple tsunami water level hazard
curves that indicate the annual probability of water level exceedance in relation to individual
scenarios.
(5) Creation of Fractile Hazard Curve
For the group of tsunami hazard curves for each point, the weight of the logic tree branches
corresponding to individual scenarios is taken into account in preparing a fractile hazard curve66that indicates the percentage of the consensus that has been obtained among experts who do notthink that the probability of exceedance given to a water level will be exceeded.
To create a fractile curve based on the annual probability of exceedance, there are the brute
force method which completely expresses all combinations of logic tree branches for each typeof fault to find the weighted mean and the Monte Carlo method which generates combinations
randomly to approximate the probability.
Expressing the process of the aforementioned numerals (1) to (5) in an equation gives thefollowing.
The results of a calculation (maximum water level) of fault l, magnitude number i, logic tree
branch j, and monitoring point k is expressed as:

h lcal,i , j , k
The probability density function of random variable h where a logarithmic normal distribution is
calculated using variance κ and logarithmic mean hcal is:p ( h; h cal ,  )Also, when the probability density function of tide level h0 is given as t(h0), the probability density
function p l,i , j , k ( h ) of water level h   hcal  h0 , which takes into account the tide level, is:pl,i , j ,k (h)  

h0max

h0  h0minp(h  h0 ; hlcal,i , j , k ,  )t ( h0 ) dh0

When variance in the calculation results and the tide level is taking into account for fault l,magnitude number i, logic tree branch j, and monitoring point k, the probability ql , i , j , k ( H th ) of
exceeding water level H

th

is:


ql , i , j , k ( H th )   th pl, i , j , k ( h) dhH

If the earthquake occurrence probability of magnitude number i on logic tree branch j is wl , i , j
and the earthquake occurrence frequency on logic tree branch j is o j , then the frequency at whichwater level H

this exceeded at fault l, logic tree branch j and monitoring point k is:

Ql , j , k ( H th )   wl ,i , j ql ,i , j , k ( H th )o j
The hazard curve (=annual probability of exceedance) f l , j , k ( H th ) for logic tree branch j inrelation to fault l and monitoring point k is:

f l , j , k ( H th )  1  e

 Q l , j , k ( H th )The annual probability of exceedance F( j1 , j2 ,, j L ), k ( H th ) for all (L units) combinations( j1 , j2 ,, jL ) of logic trees related to faults is:F( j1 , j 2 ,, j L ), k ( H th )   f l , jl , k ( H th )67

5.3.2 Calculation of Earthquake Occurrence Probability(1) Methods of Assessing Average Recurrence Interval of Characteristic Earthquakes
Modeling of recurrence intervals of characteristic earthquakes is described in Section
5.2.1(3) of the main volume. According to Table 5.2.1-2, variance of an earthquake recurrence
interval model (logarithmic standard deviation σln in a logarithmic normal distribution and α in a
BPT distribution) is about 0.2 ~ 0.4. Based on this result, it is regarded as standard to have about
three branches of logic tree for variance of earthquake recurrence intervals: 0.2, 0.3, and 0.4.
1) Case Where Data is Available on Average Recurrence Interval
In cases where the average recurrence interval of a characteristic earthquake is based ondata, a branch of logic tree is configured based on error and that is assumed to be thelogarithmic normal distribution. In a case where the true value of the distribution is x and thearithmetic mean is xo, the mean value of xo-x is zero and the standard deviation (standard errorof the distribution of true value x) is 

n . σ is the standard deviation of x. Because there iscurrently a small number of data about average recurrence interval, if the aforementioned
standard values (σln= 0.2, 0.3, 0.4) are used as the standard deviation, then the confidence
interval of the estimated values for the number of data units may be assessed. A branch of logic
tree for the average recurrence interval is configured based on the confidence interval of theestimated values relating to this earthquake recurrence interval.
In the case of a logarithmic normal distribution, the confidence interval of estimatedvalues for the number of data units pertaining to the recurrence interval is as shown in Table
5.3.2-1.
In an example of a case where the median value of the logarithmic normal distribution is

Tm and the number of data units for the earthquake recurrence interval is 1, the confidence
level of the values estimated based on variance is as follows.
Case where  ln =0.2: 0.819 Tm ~ 1.221 Tm
Case where  ln =0.3: 0.741 Tm ~ 1.350 Tm
Case where  ln =0.4: 0.670 Tm ~ 1.492 Tm
In a case where the number of data units is 5, the following results are able to be similarly
obtained.
Case where  ln =0.2: 0.914 Tm ~ 1.094 Tm
Case where  ln =0.3: 0.874 Tm ~ 1.144 Tm
Case where  ln =0.4: 0.836 Tm ~ 1.196 Tm
It is found that the confidence interval of estimated values is narrower for the case where
the number of data units is 5 than for the case where the number of data units is 1.
68

Table 5.3.2-1 Relationship between variance and confidence interval of estimated values
σln
No. of data
Confidence interval
units
0.2
0.3
0.4
Lower limit
0.819
0.741
0.670
1
Upper limit
1.221
1.350
1.492
Lower limit
0.868
0.809
0.754
2
Upper limit
1.152
1.236
1.327
Lower limit
0.891
0.841
0.794
3
Upper limit
1.122
1.189
1.260
Lower limit
0.905
0.861
0.819
4
Upper limit
1.105
1.162
1.221
Lower limit
0.914
0.874
0.836
5
Upper limit
1.094
1.144
1.196
Lower limit
0.922
0.885
0.849
6
Upper limit
1.085
1.130
1.177
Lower limit
0.927
0.893
0.860
7
Upper limit
1.079
1.120
1.163
Lower limit
0.932
0.899
0.868
8
Upper limit
1.073
1.112
1.152
Lower limit
0.936
0.905
0.875
9
Upper limit
1.069
1.105
1.143
Lower limit
0.939
0.909
0.881
10
Upper limit
1.065
1.100
1.135
*  ln : Logarithmic standard deviation of the logarithmic normal distribution2) Case Where Data is Not Available on Average Recurrence Interval
When there is no substantial information about the level of activity in submarine active
faults, a uniform distribution of 1mm/year (lower limit of activity class A) to 0.1mm/year(upper limit of activity class A) is regarded as the basis.
The mean recurrence interval is obtained by dividing the expected value of the moment
release rate per earthquake obtained from the magnitude distribution by the mean moment
accumulation rate.
Cases of uniform distribution are simple, but, in the case of the G-R type, if the upper andlower limits of magnitude are mU and mL respectively, then the probability density function of
the earthquake occurrence frequency in relation to a magnitude m where mL m mU is:f (m) βexp βm  mL 
1  exp βm U  mL 

formL  m  mU

where, β=bln10 and b are b values. In cases where the b value is unknown, it is assumed to be
0.9 which is the standard value.
3) Confidence Interval for Cases Where recurrence Interval is a Poisson Process
Commensurate with the earthquake sample period (period of time for which records areavailable) and the number of earthquake occurrences, the confidence interval for the recurrence69frequency is as shown in Table 5.3.2-2. This was prepared based on the table of confidence
intervals provided by Weichert (1980), and, when the sample period is Ts, the confidence
interval is calculated using the followings:

TS  U ~ TS  L
When there is a large number of earthquake occurrences, the confidence interval for recurrence
frequency X asymptotes to X  X .
Examples of calculations of the confidence interval commensurate with the number ofearthquake occurrence in a case where the sample period is 400 years and a case where thesample period is 1,000 years are shown in Table 5.3.2-2. For example, in a case where threeearthquakes occurred over a period of 400 years, the upper and lower limits of the number ofearthquake occurrences range between 1.37 and 5.92, and it is regarded as sufficient that threeearthquakes have occurred during a sample period of 400 years. When this is taken into
consideration, the confidence interval for the average recurrence interval is between 68 and
292 years.
Table 5.3.2-2 Confidence interval of Poisson variables (Weichert, 1980)
Number ofearthquakesthat occurred

400-year sample period

L

U

N
0
1
2
3
4
5
6
7
8
9
10
*  L and

0.00
0.17
0.71
1.37
2.09
2.84
3.62
4.42
5.23
6.06
6.89

1.84
3.30
4.64
5.92
7.16
8.38
9.58
10.8
12.0
13.1
14.3

1,000-year sample period

Lower limit

Upper limit ofLower limit

Upper limit ofof confidence

confidenceof confidence

confidence

intervalintervalintervalinterval

217.39121.21
86.21
67.57
55.87
47.73
41.75
37.04
33.33
30.53
27.97

∞
2,312.14
564.97291.97191.39140.85110.50
90.50
76.48
66.01
58.06

543.48303.03215.52168.92139.66119.33104.38
92.59
83.33
76.34
69.93

∞
5,780.35
1,412.43
729.93478.47352.11276.24226.24
191.20165.02145.14

 U : Upper and lower limits of the confidence interval for the number of earthquake
occurrences70

(2) Probability (Frequency) of Earthquake Occurrence in Hazard Analysis of Long-Term Mean
In the case of a hazard analysis of the long-term mean, the Poisson process is followed forearthquake occurrences. When this focuses on certain seismic region, it is postulated thatearthquakes occur in a random manner chronologically. In cases where the latest period of activity
is unknown and the properties of the earthquake recurrence time series are not able to be
determined, the Poisson process is applied because a probability model that takes into
consideration time renewal elements may not be applicable.
When the mean occurrence number per unit of time for earthquakes in accordance with the
Poisson process is given as ν, then probability pk that earthquakes will occur k times or more
within time period t is given using the following equation.

pk e t t k!

kTherefore, the probability that an earthquake will occur 1 or more times during time period t is:

1  p 0  1  e  t
The probability of multi-segment rupture is used for regions where it is taken into
consideration such as Tokachi-oki (off the shore of Tokachi), Nemuro-oki (off the shore of
Nemuro), Miyagi-ken-oki (off the shore of Miyagi Prefecture), close to the trench in Southern
Sanriku-oki, and other such regions. The long-term probability of multi-segment rupture is able
to be estimated based upon actual past earthquakes (multi-segment rupture rate).
In the region of both Tokachi-oki and Nemuro-oki, it has been estimated that multi-segment
earthquakes occurred during the 17th century and in the 12th to 13th centuries, and such
earthquakes have been estimated to recur at an interval of between 400 and 500 years (Central
Disaster Prevention Council, 2006). The average recurrence interval for the respective segmentsof Tokachi-oki and Nemuro-oki is about 80 years, and the ratio of multi-segment rupture is
regarded as being about 1 in 6.
In the area of Miyagi-ken-oki and close to the trench in Southern Sanriku-oki, there has been
one multi-segment rupture earthquake that occurred of the two earthquakes that struck close to
the trench in Southern Sanriku-oki (1897 and 1793), and the ratio of multi-segment rupture is
regarded as being about 1 in 2.
(3) Probability of Earthquake Occurrence in Hazard Analysis at Current Time
When the logarithmic normal distribution and BPT distribution taking into account theperiodicity of earthquakes to individually assess the probability of earthquake occurrences in the
future over t period of years, the assessment needs to be carried out in the following method.
BPT distribution takes into account irregularity in the stress accumulation process, and71

corresponds to a model where an earthquake occurs when the accumulation of stress reaches acertain level, and the probability of an earthquake occurrence is calcutlated using variance α
pertaining to the seismic interval and mean seismic interval T f t    2 2t 3

pertaining to earthquakes.

 exp t   2 t  , t ≧ 0
12

2

2

In so doing, the probability of the next earthquake occurrence from time T to ΔT years later is:T  TP T , T    f ( t ) dtT

 f (t )dt
TBelow, an example is shown where the BPT distribution is used to assess the probability of theearthquake occurrence over a period of 50 years beginning with 2015 as the first year.
Ex.: If the average recurrence interval is 75 years and the time of latest activity is September 26,
2014, then:

There are 0.2657 years from the time of latest activity through the initial year of 2015,
so T=0.2657 is assumed.



If α=0.3 is assumed, then when the aforementioned equation is solved based on ΔT=50
and T=0.2657, P(T,ΔT) =0.11 is given. In other words the probability of the earthquake
occurrence over a period of 50 years beginning from the initial year of 2015 iscalculated to be 11%.

In cases where the BPT distribution is used to calculate the rupture probability of eachsegment and the multi-segment rupture is taken into consideration, then the rupture probabilityof multi-segment is calculated using the method discussed in Section 5.2.1 of the main volume
and is different from the case of a long-term mean. An example is given below.
Ex.: In a case where the rupture probability over the next 30 years for two segments (A and B)
is 20% for both and the two segments have ruptured at a rate of 1:6 times in the past.
1) Method described in a preliminary version by the Headquarters for Earthquake Research
Promotion:(i) The probability of earthquakes simultaneously during the target period is calculated.
0.2×0.2= 0.04(ii) The resulting probability is multiplied by the rate of multi-segment rupture.
0.04×1/6 = 0.007 = 0.7(%)
2) Revised WGCEP method(i) In the case of multi-segment earthquakes, half of the mean recurrence probability of past72

earthquakes is assumed (=1/12).
0.2×1/12(ii) In the case of single earthquake, the recurrence probability × rate of single earthquake isassumed.
0.2×5/6 = 0.17(iii) The remaining portion is allocated so that the number of earthquakes is the minimum.
So that the number of earthquakes for the remaining portion is set at the minimum, multisegment earthquakes is assumed for all. Accordingly, the probability of multi-segment rupture
is: 0.2×1/12 + 0.2×1/12 = 0.033 = 3.3(%).
5.3.3 Configuration of Earthquake Occurrence Model and Tsunami Propagation Model(1) Occurrence Region
The tsunami sources region that are subject to assessment are appropriately configured bytaking into account the impact on assessment points. When variance in the tsunami height
estimates is taken into account, it is sufficient that tsunami sources having a significant impact
on the probability of exceedance of the targeted water level be regarded as subject to assessment,
so it is possible that the composition of the tsunami group reflected in the analysis may change
according to the targeted water level. For example, there is an approach where, when calculations
are performed using a case where a tsunami becomes the largest within a seismic region (dipangle and rake angle), seismic regions where the maximum water level ascent (descent) H in
front of the assessment point is:|X|>|H|∙κ2.3
are not subject to assessment because the only influence on the probability that the water level
will be exceeded is on the order of -2 or less of the earthquake occurrence frequency. Where, X is
the water level subject to assessment (site height and height at which water may be drawn), and κ
is the variance included in the tsunami height. In such a case, even if variance included in tsunami
height is assessed, the ultimate impact on the probability of tsunami water level exceedance isregarded as being minuscule. Also, if there is a dominant tsunami source in relation to the hazard,
then it is also possible that the relative importance of other occurrence regions or tsunami sources
may decrease.
(2) Earthquake Occurrence Model
The basic approach to configuring tsunami source models is shared with the deterministic
tsunami hazard analysis presented in Chapter 4 of the main volume. However, in cases where
uncertainty in the parameters dominant in the probability of the targeted water level being73

exceeded is reflected in the analysis, uncertainty about other parameters whose impact is minimal
does not need to be included in the analysis.
(3) Tsunami Propagation ModelIn the assessment of phenomenon where tsunami propagate and phenomenon where tsunami
inundate, calculation accuracy and other such elements are taken into account so that such
hydraulic phenomena are able to be appropriately expressed in selecting the governing equationand numerical scheme as well as configuring the initial conditions and boundary conditions. The
basic approach to these elements is presented in Chapter 6 of the main volume.
In cases where the purpose is to design structures, which includes conducting assessments
for the purpose of designing the height of seawalls or other such structures on the basis ofprobabilistic tsunami hazard analyses, it is not necessary that the area around the assessment pointreflect the current topography, and it is possible to construct a model, including one where theboundary conditions of the coastline are a vertical wall of unlimited height.
5.3.4 Calculation of Tsunami Height Distribution(1) Implementation of Tsunami Simulations
The median value of the tsunami height in front of the power plant is needed for all scenarios
comprising the branches of a logic tree. The median value is the maximum water level ascent(descent) in front of the power plant that is able to be obtained from numerical simulations oftsunami in accordance with the scenarios.
(2) Consideration of Variance
When the median value has been obtained, various types of errors contained in tsunami
simulations are taken into account in calculating the probability distribution of true values(tsunami height that actually strikes the power plant when an earthquake occurs that is in keepingwith the scenario). For this, variance κ of the tsunami height included in the scenarios is used.
The probability distribution obtained at this stage is a conditional probability when an earthquake
as described in the scenario occurs.
The formula for the probability density function of logarithmic normal distribution is givenin the following equation, so it is sufficient to apply the logarithm for the median value to μ andthe logarithm for κ to σ. For example, in a scenario where a branch of logic tree is selected that
holds that “a phenomenon that reaches 1% on both sides of the distribution does not actuallyoccur”, 1% from both sides of the distribution is cut.

74Probability density
function

Time
Tsunami simulation results(Highest or lowest value)

Logarithmic normal
distribution using
variance σ aroundmedian value h0

Probability when tsunami waterlevel is h

Figure 5.3.4-1 Illustration of consideration of variance in median value
Furthermore, the distribution of the probability of exceedance may be computed by
calculating the probability of exceedance for each tsunami height based on the probability density
function (Figure 5.3.4-2).

Area of the oblique line
= Probability that water level will exceed hdue to tsunami= Probability that tsunami height will be
exceeded

Probability density
function
Probability
when tsunami
water level ishDistribution of
exceedance
Probability thattsunami height does
not exceed hArea plotted by sequentiallychanging hProbability thattsunami height
does exceed hFigure 5.3.4-2 Concept of distribution of probability of water level exceedance
5.3.5 Consideration of Tide Level Distribution(1) Configuration of Tidal Data
Tide level may be regarded as a random variable that follows a frequency distribution. The
probability density function of the tide level may be calculated by using appropriately obtainedtide level records of the area around the power plant and processed in the following method.
75

Specific details on the impact that high tide has on the results of a probabilistic tsunami
hazard analysis are given in Section 5.4 of the appendix volume.
1) Case Where Tide Level Records are Available for a Long Period of TimeIn a case where records are available about tide levels over a long period of time for thearea around the power plant, the tide levels are divided into segments to create a distributionof tide level frequency for each segment from the time history data. If the ratio is multiplied sothat the area of the tide level frequency distribution diagram is 1, then this will be theprobability density function for tide levels.

Tide level

Record of tide levels around power plant

Time

Frquency

Distribution of tide level
frequency

Schematic
representation
Function

Incidenceprobability

Statisticalprocessing
Probability density function for tide
level

Tide level

Figure 5.3.5-1 Procedure for converting time history records of tide levels to a probability density
function
2) Case Where Only Tidal Harmonic Constant is Available
Tide level records include both astronomical tides that occurred on account of thepositional relationship of the earth, moon and sun, as well as meteorological tides which mainly
include the effects of atmospheric pressure, and the former are periodical. With tide levels usedin probabilistic tsunami hazard analysis, it is desirable to include meteorological tides in orderto represent actual tide levels in the area around the power plant. However, in cases whereappropriate records of tide levels over the long term are not able to be acquired, it is possible
to re-create time history data for astronomical tide levels based on the tidal harmonic constantfound from automatic tide-gauge stations near the power plant. However, in such a case,76attention needs to be given so that meteorological tides are not included.
The equation for re-creating tide levels based on the harmonic decomposition value isshown below (Japan Coast Guard, 1992).
Tide level  t    f i H i  cosVi  u i    i   Z

Vi  u i   V0i  u i   n  L   i  S    i  t
Subscript i represents the types of component tide, and Σ indicates the sum of the componenttides.
where,

f i , ui

: Correction for amplitude and phase

Hi ,  i: Amplitude and lag calculated based on measured values of tides(harmonic decomposition value)Vi: Astronomical parameter(subscript 0 represents 0:00UT)n: Subscript for component tide symbol (ex. n  2 when there areM2 component tide)L: Longitude (west longitude+, east longitude-)i: Angular velocity of component tideS

: Time difference ( S  9 at Japan standard time)Z: Mean water surface height (height based on basic level surface)(2) Synthesis of Tide and Calculation Results
In an ordinary tsunami hazard analysis, it is possible to finally take into consideration tidelevel distribution after a tsunami hazard curve has been obtained. A method for considering tidelevel distribution in a tsunami hazard curve is shown in Figure 5.3.5-2. Tide level distribution is
given as (a), the tsunami hazard curve in a case where the tide level distribution is not taken into
account is given as (b), and each of these converted to the segment frequency is shown as (c) and(d), respectively. Adding together the (c) and (d) distributions gives (e), and, when this isconverted into a cumulative form, the result is (f).

77

Probability
density
確率密度

Annual occurrence
frequency
年発生頻度

(a)

Tide level(b)

Tsunami height (m)(c)
Segment
frequency
区間頻度

Segment
relative frequency
区間相対頻度(d)Tide level

Tsunami height (m)Segment
frequency
区間頻度

Annual occurrence
frequency
年発生頻度

(e)

Tsunami height (m)(f)

Without tide level consideration
With tide level consideration

Tsunami height (m)Figure 5.3.5-2 Method of considering tide level distribution in assessment of tsunami hazard curve785.3.6 Creation of Fractile Curve
The final result of probabilistic tsunami hazard analysis is the frequency that reaches a specifictsunami height (annual probability of exceedance) at a specific site, and the percentage to which a
consensus can be reached among experts, who view this level as not being exceeded, is arranged as aparameter (for example, a curve that indicates an annual probability of exceedance where 80% of theexperts find that it will be smaller than this is referred to as 80% fractile).
In other words, the abscissa of a fractile hazard curves is the tsunami height (maximum waterlevel or minimum water level), and the ordinates is the annual probability of exceeding this tsunami
height (1/year(s)), and several curves are drawn using the ratio (%) of the consensus as a parameter.
It is also possible to draw mean hazard curve by determining the weighted arithmetic mean foreach scenario. In the case of the weighted arithmetic mean, sometimes a scenario with very small
weight but extremely high probability of exceedance will significantly raise the probability. However,
because there is also the advantage that results are easy to intuitively understand and the issue of whatshould be appropriate fractile is unavoidable, both fractile and mean hazard are calculated in the caseof a probabilistic tsunami hazard analysis.
Although the method to calculate fractile hazard curves from hazard curves is shown in Figure
5.3.6-1, fractile curves may actually be calculated according to the following procedure.
・Curves of the annual exceedance probability (hazard curves) are rearranged in descendingorder for each targeted tsunami height.

・Counting from the largest, the exceedance probability of hazard curves at N% is given as
the N% fractile.
Distribution function ofweightDistribution of annual
exceedance probability

Along the H=h0 line, W ofintersecting lines is read

85% fractile
50% fractile
15% fractile

Total for strength of scenarios
where the probability ofexceeding tsunami height h0 is
below P

Cumulative
sum of weight
Cumulative sum of
weight is calculated

Fractile hazard curves
Plotted by changing h0(Drawn for each h0)(Drawn for each h0)

Total for strength of scenarios
where the probability ofexceeding tsunami height h0
is below P0

Figure 5.3.6-1 Method to calculate fractile hazard curves from hazard curves
79

The specifics of the algorithm for calculating fractile curves are shown below, and two methods
for randomly creating branches of logic tree (brute-force method and Monte Carlo method) are also
indicated.
(1) Brute-Force Method
The reordering of F( j1 , j2 ,, jL ),k ( H th ) from lowest to highest value is expressed as Fj,k (H th ) ,and the weight of logic tree branch j  is given as vj   l vl , jl . J is adopted so that to satisfy(Figure 5.3.6-2):
J 1J v  V   vj  1j

j  1jThen, the V  100% fractile curves G k ( H th ) are given as:

Gk (H th )  FJ,k (H th )Annual probability ofexceedance

Cumulative weight

Figure 5.3.6-2 Concept using the brute-force method to convert annual probability of exceedance tofractiles(2) Monte Carlo method
For each fault l, uniform random numbers are produced so that logic tree branch j l is
adopted with probability v l , jl . (If 1 v l , j  uniform random number  1 vl , j , then logic
jl 1

jl

tree branch j is adopted)
This is repeated for all faults, and80

F( j1 , j2 ,, jL ),k ( H th )   f l , jl ,k ( H th )lis calculated.
By repeating this operation, the values of F( j1 , j2 ,, jL ),k (H th ) will be assembled. Because thegenerated combinations of ( j1 , j 2 ,  , j L ) have taken into account weight, F( j1 , j2 ,, jL ),k ( H th )may be regarded as having a uniform weight (see Figure 5.3.6-4). Accordingly, for example, if
100 units are calculated for F( j1 , j2 ,, jL ),k ( H th ) using the Monte Carlo method, the value of the
20th, counting from the larger side will be the value for the 80% fractile.

Figure 5.3.6-3 Monte Carlo method81

Annual probability ofexceedance

Cumulative weight

Figure 5.3.6-4 Concept using the Monte Carlo method to convert annual probability of exceedance tofractiles[Chapter 5 References]
Aida, I. (1977): Simulation of Large Tsunamis Occurring in the Past off the Coast of the Sanriku
District, Bulletin of the Earthquake Research Institute, The University of Tokyo, Vol. 52, pp.
71-101 (in Japanese).
Annaka, T. and H. Yashiro (2000): Uncertainties in a probabilistic model for seismic hazard analysis
in Japan, Risk Analysis II, WITPRESS, Boston, pp. 369-378.
Annaka, T., M. Shimada and T. Hiroshige (2001): Uncertainty Assessment Method for Earthquake
Hazard Curves Based on the Monte Carlo Method, Japan Society of Civil Engineers 56th
Annual Scholarly Lecture Meeting, I-A016, pp. 32-33 (in Japanese).
Annaka, T., T. Suehiro and T. Hiroshige (2002): Uncertainty Assessment Method for Earthquake
Hazard Curves Based on the Monte Carlo Method, The 11th Japan Earthquake Engineering
Symposium, No. 15, pp. 73-78 (in Japanese).
Annaka, T., K. Satake, T. Sakakiyama, K. Yanagisawa and N. Shuto (2006): A Method of Probabilistic
Tsunami Hazard Analysis, The 12th Japan Earthquake Engineering Symposium, No. 13, pp.
158-161 (in Japanese with English abstract).
Annaka T., K. Satake, T. Sakakiyama, K. Yanagisawa and N. Shuto (2007): Logic-tree Approach for
Probabilistic Tsunami Hazard Analysis and its Applications to the Japanese Coasts, Pure andApplied Geophysics, Vol. 164, pp. 577–592.
Atomic Energy Society of Japan (2012): Implementation Standard Concerning the Tsunami
82

Probabilistic Risk Assessment Due to Tsunami on Nuclear Power Plants: 2011 (in Japanese).
Cabinet Office Nankai Trough Massive Earthquake Model Review Committee (2012): Nankai
Trough Massive Earthquake Model Review Committee (Second Report) Tsunami Fault
Model Compilation: Tsunami Fault Models and High Tsunami and Flooding Areas, etc. (inJapanese).
http://www.bousai.go.jp/jishin/nankai/model/pdf/20120829_2nd_report01.pdf (Accessed on
August 2016)
Central Disaster Prevention Council Expert Panel on Subduction-Zone Earthquakes Near the Japanand Kuril Trenches (2006): Report of the Expert Panel on Subduction-Zone Earthquakes Near
the Japan and Kuril Trenches (in Japanese).
Ellsworth, W.L., M.V. Matthews, R.M. Nadeau, S.P. Nishenko, P.A. Reasenberg and R.W. Simpson(1999): A Physically-based Earthquake Recurrence Model for Estimation of Long-term
Earthquake Probabilities, Workshop on EARTHQUAKE RECURRENCE: STATE OF THE
ART AND DIRECTIONS FOR THE FUTURE, Istituto Nazionale de Geofisica, Rome, Italy,
pp. 22-25.
Geist, E. and T. Parsons (2006): Probabilistic Analysis of Tsunami Hazards, Natural Hazards, Vol. 37,
pp. 277-314.
Gutenberg, B. and C.F. Richter (1944): Frequency of earthquakes in California, Bulletin of the
Seismological Society of America, Vol. 34, No. 4, pp. 185-188.
Headquarters for Earthquake Research Promotion Earthquake Research Committee (2001): Methods
for Assessment of Long-Term Earthquake Occurrence Probability (June 8, 2001, in Japanese).
Headquarters for Earthquake Research Promotion Earthquake Research Committee (2005): LongTerm Assessment of Nobi Fault Zone (January 12, 2005, in Japanese).
Headquarters for Earthquake Research Promotion Earthquake Research Committee (2011): LongTerm Assessment of Earthquake Activity from Area Offshore of Sanriku to Area Offshore of
Boso (Second Edition) (November 25, 2011, revised on February 9, 2012, in Japanese).
Headquarters for Earthquake Research Promotion Earthquake Research Committee (2014):
Nationwide Seismic Ground Motion Prediction Map 2014 Version: Survey of Seismic Ground
Motion Hazards Nationwide (December 19, 2014, in Japanese).
Japan Coast Guard (1992): Japan Coastline Tidal Harmonic Constant Table (in Japanese).
Japan Nuclear Energy Safety Organization (2014): Guide to Formulation of Reference Tsunami Basedon the Probabilistic Method.
Japan Society of Civil Engineers Nuclear Civil Engineering Committee (2011): Methods for
Probabilistic Tsunami Hazard Analysis (in Japanese).
http://committees.jsce.or.jp/ceofnp/node/39(Accessed on August 2016)
83

Kurita, T., M. Matsuyama and D. Uchino (2013): Uncertainty of Numerical Tsunami Simulation
Evaluated in Comparison with the Field Survey Results of the 2011 Tohoku Earthquake
Tsunami, Journal of Japan Society of Civil Engineers B2 (Coastal Engineering), Vol. 69, No.
2, pp. I-216 - I-220 (in Japanese with English abstract).
Mabuchi, H., M. Ohtake and H. Sato (2002): Possibility of Estimating the Maximum Earthquake
Magnitude Based on a Modified G-R Model for Magnitude-Frequency Distribution: Spatial
Distribution of Mc East off Northeast Japan, Zisin, Journal of the Seismological Society ofJapan, Second Series, Vol. 55, pp. 261-273 (in Japanese with English abstract).
Matthews, M.V., W.L. Ellsworth and P.A. Reasenberg (2002): A Brownian Model for Recurrent
Earthquakes, Bulletin of the Seismological Society of America, Vol. 92, No. 6, pp. 2233-2250.
Ministry of Construction’s Public Works Research Institute Earthquake Hazard Department
Earthquake Vibration Research Office (1983): Survey of Frequency and Magnitude ofForeshocks and Aftershocks, Public Works Research Institute Material, No. 1995 (in Japanese).
Murotani,S., K. Satake and Y. Fujii (2013): Scaling Relations of Seismic Moment, Rupture Area,
Average Slip, and Asperity Size for M~9 Subduction Zone Earthquakes, Geophysical Research
Letters, Vol. 40, pp. 5070-5074.
Odagiri, S., and K. Shimazaki (2000): Size of the Historical Earthquake Which Occurred on an Active
Fault in Japan, Zisin, Journal of the Seismological Society of Japan, Second Series, Vol. 53,
pp. 45-56 (in Japanese with English abstract).
Shimazaki, K., K. Kawase and G. Aoki (1998): One Model for Configuration of Activity Segments inLong and Highly Active Fault System, Seismological Society of Japan Fall Meeting
Proceedings, C52, p. 112 (in Japanese).
Sugino, H., Y. Iwabuchi, N. Hashimoto, K. Matsusue, K. Ebisawa, H. Kameda and F. Imamura (2014):
The Characterizing Model for Tsunami Source regarding the Inter-plate Earthquake Tsunami,
Journal of Japan Association for Earthquake Engineering, Vol. 14, No. 5, pp. 1-18 (in Japanesewith English abstract).
Sugino, H., Y. Iwabuchi, M. Nishio, H. Tsutsumi, M. Sakagami1 and K. Ebisawa (2008):
Development of Probabilistic Methodology for Evaluating Tsunami Risk on Nuclear Power
Plants, The 14th World Conference on Earthquake Engineering, October 12-17, 145 2008,
Beijing, China.
Sugiyama, Y., (1998): Current State of Research on Active Faults and Ancient Earthquakes andFuture Issues, Geology News, No. 523, pp. 12-20 (in Japanese).
Utsu,T. (1971): Aftershocks and earthquake statistics (III) - Analyses of the Distribution ofEarthquakes in Magnitude, Time, and Space with Special Consideration to Clustering
Characteristics of Earthquake Occurrence (1)-, Journal of the Faculty of Science, Hokkaido
University, Vol. VII, No. 5, pp. 379-441.
84

Weichert, D. H. (1980): Estimation of the earthquake recurrence parameters for unequal observation
periods for different magnitudes, Bulletin of the Seismological Society of America, Vol. 70,
No. 4, pp. 1337-1346.
Wesnousky (1994): The Gutenberg-Richter or Characteristic Earthquake Distribution, Which Is It?,
Bulletin of the Seismological Society of America, Vol. 84, No. 6, pp. 1940-1959.
WGCEP (1995): Seismic hazards in southern California: probable earthquakes, 1994 to 2024, Bulletinof the Seismological Society of America, Vol. 85, No. 2, pp. 379-439.

85

Chapter 6 Numerical Simulation Methods
6.1 Simulation of Tsunami Propagation and Run-up
6.1.1 Basic Concepts(1) Selection of Numerical Model
For assessing the phenomenon of tsunami propagation and run-up, it is important to take into
account calculation accuracy and other such elements so that hydraulic phenomena may beappropriately expressed and to select the governing equations and numerical scheme, as well as toconfigure the initial conditions and boundary conditions.
The method of selecting the numerical model will be discussed in detail in Section 6.1.2 ofthe main volume.
(2) Execution of Numerical Simulation
The computation domain, grid size, computation time step, bathymetry data, structure data,
coefficients in governing equations, and simulating time are appropriately determined according
to the spatial tsunami shape and topography of the sea areas along with the sources and target site.
The execution method of the numerical simulation will be discussed in detail in Sections 6.1.3
and 6.1.4 of the main volume.
6.1.2 Selection of Numerical Model
6.1.2.1 Governing Equations and Numerical Scheme(1) Governing Equations for Tsunami evaluation
Since the tsunami has a longer wavelength as compared to the water depth, the long-wave
theory is applied. The theories often used for calculating tsunami propagation are governing
equations for two-dimensional field derived by integrating three-dimensional governing equationsin the vertical direction from the bottom to the surface of the water, and are divided into three
types: linear long-wave theory and nonlinear long-wave theory integrated on the assumption ofhydrostatic approximation, and the dispersive wave theory integrated by taking into account wave
curvature but not assuming hydrostatic approximation. When calculating tsunami propagation, thecharacteristics of the following theories need to be understood and then appropriately selected inaccordance with the objective phenomena.
In recent years, as fluid analysis technology has developed it is becoming increasingly86possible to also apply three-dimensional fluid analysis models (hereinafter, “three-dimensionalmodels”) that directly calculate a three-dimensional governing equation. Because it is conceivablethat in the future there will be a practical three-dimensional model thanks to further advances madewith computers, a summary is also provided of three-dimensional models in Section 6.1.4 of themain volume.
1) Linear Long-wave Theory
This is applied under the condition that the ratio of the wave height to the water depth issufficiently small. The momentum equation comprises an unsteady term and a pressure term
(hydrostatic distribution). When the bottom friction cannot be ignored, a friction term should
be considered.
2) Nonlinear Long-wave Theory (Shallow Water Wave Theory)
This is applied under the condition that the ratio of the wave height to the water depth isnot small (the nonlinearity cannot be ignored). The momentum equation comprises an unsteadyterm, an advection term, and a pressure term (hydrostatic distribution); with these terms, thesteepening of the wave front in shallow water can be considered. In general, since friction withthe sea bottom cannot be ignored, a friction term is expressed. The horizontal eddy viscosity
term may be considered if necessary.
3) Dispersive Wave Theory
This is applied under the condition that the curvature of the tsunami wave increases withpropagation, the vertical acceleration of the water particles cannot be ignored, and wave
variance appears. The momentum equation comprises the unsteady term, the advection term,
the pressure term, and the variance term, and the variance term is derived by not utilizinghydrostatic approximation in the process of integration. The dispersive wave theory includes alinear dispersive wave theory that focuses on deep sea areas such as calculation of the far-fieldtsunami propagation, and nonlinear dispersive wave theory that focuses on shallow sea areas
such as calculation of near-field tsunami. However, linear long wave theory may be applied incases where the effect of variance is small even for far-field tsunami (Yanagisawa et al., 2012).
As the tsunami propagates in a shallow water area, depending on the conditions such aswave shape and water depth, the synergetic effect of the nonlinear effect in which the wave
peak is inclined forward and the variance effect in which short waves of the cycle are left
behind from the wave body as a result, the phenomenon that the tsunami body splits into
multiple waves with a short period and the wave height is amplified may occur. This is called
soliton fission. If a tsunami is accompanied by soliton fission, wave breaking occurs before or87

after run-up. Even if the soliton fission had forced an increase in the run-up heights, this factor
is accordingly taken into account by setting the slip of the fault model to be larger, provided
the run-up heights were derived from calculations using the same governing equations andnumerical scheme employed in setting the fault. Consequently, in discussing the water level,
the nonlinear dispersive theory might not be needed in principle. The variance term has theeffect of suppressing the leaning of wave front. Therefore, there is also an idea that using
dispersive wave theory more consistently than deep water region without limiting to the soliton
fission wave generation region can more accurately evaluate the water level change in the coast
area including the split start position (Iwase et al., 1998; Hara et al., 1998). There are also
examples where the usefulness of this theory has been verified by including a damping term
due to wave breaking and applying this to practical numerical simulations (Nuclear Civil
Engineering Committee Tsunami Evaluation Subcommittee, 2007).
The index of variance effect by Iwase et al. (2002) serves as an evaluation criterion thattakes into consideration the impact of the variance effect in deep sea regions, and examples ofdetailed reviews are given in Section 4.1.4.2 of the appendix volume.
(2) Governing Equations and Numerical Scheme for Near-field Tsunami Propagation
1) Nonlinear Long-wave Theory
For nearshore tsunami propagation, where the water depth is shallower than 200m, thegoverning equations of the nonlinear wave theory should be selected (Shuto, 1986). In such acase, an explicit finite difference scheme with a staggered leapfrog method is generally adopted
because the analysis method of the numerical error caused by the finite difference scheme isnearly established.
In actual practice, either the method of Goto and Ogawa (1982) (hereinafter referred to as
the Goto method, see Section 4.1.1 of the appendix volume) or the method of Tanaka (1985)(hereinafter referred to as the Tanaka method) is applied. Both are nonlinear wave theories, buthave slight differences as shown in Table 6.1.2-1.
However, since it has been verified that there is very little difference between bothmethods except under special conditions when the sea bottom slope is less than 1/100 and theperiod is less than 5 minutes, the use of either method does not pose a practical problem.
In addition, it is possible to apply the finite element method or other numerical simulation
method. In such a case, it should be verified that the accuracy of the method is equal to or
better than that of the abovementioned method by a prior analysis of the numerical error.

882) Nonlinear Dispersive Wave Theory
In the design of structures in cases where the structure is subject to the impact of anincrease in tsunami force due to soliton fission, such as breakwaters erected in the offing, anonlinear dispersive wave theory is used to take into consideration such impact.
In the “Tsunami-Resistant Design Guideline for Breakwaters” (Ministry of Land,
Infrastructure, Transport and Tourism, 2013), it is stated, “The condition to consider this is thatthe incident tsunami height is generally at least 30% of the water depth (the tsunami height bynumerical simulation is at least 60% of the water depth) and the sea bottom slope is shallow at

Numerical scheme

Governing
equation

about 1/100 or less”.
Table 6.1.2-1 Comparison between Goto method and Tanaka method
Goto method
Tanaka method
Advection term
Conservation typeNon-conservation type
Friction term
Manning type
General friction type
Horizontal eddy
viscosity term

Introduced if necessary

Introduced

Alignment ofvariables

Staggered scheme

Staggered scheme

Leapfrog scheme(Discretization error has
accuracy to the second degree
because both space and time arefrom a central difference.)
1st-order upstream difference
scheme with accuracy of 1storder

Leapfrog scheme(Discretization error has
accuracy to the second degree
because both space and time arefrom a central difference.)

Difference inpressure term

Difference inadvection term
Difference infriction term
Difference inhorizontal eddy
viscosity term

Approximated implicitly-

Lax-Wendroff scheme withaccuracy of 2nd-order
Approximated explicitly (timeforward difference)
Approximated explicitly (timeforward difference)(3) Governing equations and numerical scheme for the far-field propagation of tsunamis
In the case of the far-field propagation of a tsunami, the linear theory can be applied because
the wave height is small when compared to the water depth. However, when the initial tsunami
profile has a wide range with respect to the frequency components, the wave velocity varies
slightly for each frequency at the deep water; further, since it propagates for a long time, the delayof the shorter wave is larger. Therefore, in order to reproduce this effect, it becomes necessary toapply governing equations that include the variance term. Furthermore, for far-field tsunamis, theCoriolis force must be considered in the momentum equation. In addition, since the effects of the89spherical earth cannot be ignored, a spherical coordinate system must be adopted. For a numerical
scheme, the alignment of variables is performed by a staggered leapfrog scheme while the explicit
difference method is adopted for the equation of continuity. An implicit difference calculus isgenerally adopted for the momentum equation (see Section 4.1.2 of the appendix volume).
6.1.2.2 Initial Conditions(1) Distribution of vertical displacement on the Sea Bottom
The distribution of vertical displacement on the sea bottom - the initial condition for thenumerical simulation of the tsunami - is generally evaluated by using the Mansinha and Smylie(1971) method (see Section 4.2 of the appendix volume) and the Okada (1985) method. Thesemethods are based on the theory of elasticity under the conditions of isotropy and homogeneity.
Therefore, it is often the case that calculation of distribution of vertical displacement is performedby these methods for both near-field tsunami and far-field tsunami.
The aforementioned methods treat ground structures as homogeneous, when examining theinfluence of the three-dimensional underground structure on the tsunami, the method by theseafloor crustal movement analysis that can consider the three-dimensional heterogeneous
structure can be applied (see Section 4.2.2 of the appendix volume) (Tsuchiya et al., 2013).
(2) Continuance time of displacement
The duration of the fault movement that generates a tsunami is assumed to be approximately
several 10s to 120s. In such a case, the continuance time of displacement has no significant effecton the results of the numerical simulation of the tsunami as compared to the case in which the sea
bottom is displaced instantaneously (Aida, 1969; Iwasaki and Yang, 1974). Consequently, both themethods - with and without a consideration of the continuance time of displacement - may be
applicable.
When an instantaneous distribution of vertical displacement is assumed on the water surface,a short-period oscillation might occasionally occur in the numerical results. This oscillation canbe ignored if it disappears when the continuance time of displacement is considered. Also, as seenin the 2011 Tohoku earthquake, 2004 Sumatra earthquake, when some large earthquakes may havethe capability of generating tsunamis due to multiple large fault breaks, the rupture time of fault
reaches several hundred seconds or more. For example, in the Cabinet Office (2012), fault rupture
velocity propagated from the rupture point and the continuance time of fault displacement (risetime) have been taken into consideration in heterogeneous tsunami source models.

90

(3) Setting the Initial Conditions
The distribution of vertical displacement on the sea bottom in Section (1) is generally given
for the initial water surface as an initial condition. When considering the time change of seabedground fluctuation, the hydrostatic surface is taken as the initial water level condition. Also,
because the dip angle of faults around the trench is quite small, horizontal displacement is larger
than vertical displacement. For this reason, tsunami resulting from horizontal displacement in theseafloor slope can no longer be disregarded. Tanioka and Satake (1996) took into consideration
the effect on the water level attributable to horizontal displacement in the seafloor slope.
In any of the above cases, there is no initial velocity due to the tsunami.
6.1.2.3 Setting the Boundary Conditions(1) Offshore Boundary Conditions
Since the computational region is finitely determined, open boundaries are artificiallyprovided on the offshore and lateral sides. Appropriate boundary conditions need to be applied sothat the behavior of the tsunami is free from the artificial reflection from the boundaries. The
offshore boundary and twolateral side boundaries are referred to as the offshore boundaries.
1) Boundary conditions for a tsunami propagating from the inner to the outer areas of thecomputational region:
As the boundary conditions in a case where there is a wave source region with in theanalysis region, free transmission conditions (Goto and Ogawa, 1982) may be assumed, which
are derived based on the method of characteristics. Also, by configuring appropriate parameters,
nonreflecting boundary conditions (ex., Cerjan et al., 1985) and other such conditions may be
applied.
The other free transmission conditions can be considered by setting a virtually complete
reflecting wall at the open boundary. The transmitted wave height at this boundary is assumed
to be one half of the standing wave height at the virtually complete reflecting wall (Hino andNakaza, 1988). In such a case, if the wall is properly positioned, results can be obtained withhigh accuracy (Imamura et al., 2001).
Both the methods, i.e., the method of characteristics and that of the virtually complete
reflection wall, can be applied to the case in which the tsunami propagates from the outer tothe inner areas of the computational region.
2) Method of inputting a tsunami at the offshore boundary in the near-field ocean:
In case of the calculation of a far-field tsunami in the coasts of Japan, the tsunami motion91

is calculated in accordance with the linear long-wave theory or the linear dispersive wave
theory formulated using the spherical coordinates system under the initial condition that was
obtained using the tsunami source model. The incident tsunami component may be used forthe offshore boundary of the computational region in the near-field domain.
The time series of tsunami estimated from tide observation data can be used as an input
for the offshore boundary condition.
(2) Onshore Boundary Conditions
The boundary conditions between the sea and land should be applied in accordance with thefollowing conditions.
1) Full Reflection Conditions
When the tsunami run-up onto land is not considered, a vertical wall with an infinite
height should be positioned on the coastal line, and the flow rate per unit width in the direction
perpendicular to the coastal line should be assumed to be zero. In other words, a complete
reflection condition should be applied. However, when this condition is applied, the water
depth must be sufficient so that the sea bottom at the seaside region adjacent to the coastal line
is not exposed during the run-down of the tsunami. If the water depth is low, the boundary
conditions at the run-up front, which are discussed in the following section, can be used bytaking the exposure of the sea bottom during the run-down into account.
2) Wave front Conditions
When considering the tsunami run-up onto sloping land or run-down into a shallow sea
exposing the sea bottom, the topography is approximated in the form of steps with the meshsize, and the existence of water in the topography at the tsunami front is judged at every time
step. Kotani et al. (1998) proposed a method that improved on that of Iwasaki and Mano (1979),
and has been extensively used in practical works (see Section 4.3 of the appendix volume).
This method can be summarized as follows:・The tsunami front is located at the boundary between the cell in which the sum of thewater depth and maximum still water depth at the cell boundaries (four sides) is
positive, and the cell in which the sum is either zero or negative.

・The total water depth for calculating the flow rate per unit width is given as thedifference between the water level of the wave front and the bottom height in theneighboring cell. When this difference is negative, the flow rate per unit width should
be assumed to be zero (no run-up).

・

When calculating advection term, in cases where the total water depth is zero or less92

than a certain minimum value, only term where the total water depth has adenominator are omitted in calculating the advection term.
(3) Overflow Boundary Conditions
The boundary conditions for the case in which the tsunami flows over the breakwater, sea
dike, seawall revetment, and other structures should be applied according to the following
conditions.
1) When the breakwater, etc., are modeled by the ground height as a part of the topography:
In this case, the boundary conditions at the run-up front described in the previous section
can be applied to the boundary conditions in which the tsunami flows over the breakwater, etc.
2) When the breakwaters, etc., are modeled by the boundaries between cells:[1] Honma Model (Honma, 1940)
When breakwaters or sea dikes exist in the computational region and the water levelexceeds the crest elevation, the overflow rate per unit width is estimated using the following
formulae in accordance with the overflow conditions (Iwasaki et al., 1981; Goto and Ogawa,1982).
(Complete and incomplete overflows)q   h1 2 gh1

h2 

2
h1
3

(Submerged overflows)q   h2 2 g h1  h2 

h2 

2
h1
3

where h1 and h2 are the water depths in front of and behind the structure on the top of thestructure, respectively, = 0.35, ' = 2.6, and g is the gravitational acceleration. If the water
does not flow over the breakwater and sea dike, the complete reflection condition setting of
the vertical wall is assumed and the flow rate per unit width in the direction perpendicular tothe structures is assumed to be zero.

93[2] Aida Model (Aida, 1977a)
When a seawall exists on the coastal line, the volume of overflow onto the dry bed of theseawall can be estimated using the following broad-crested weir formula and the flow rate
coefficient as is the case with a submerged breakwater.
q  C1H1 gHwhere H1 is the water level on top of the revetment; ΔH is the water level difference at thediscontinuous position; and C1=0.6.

q

h1

h2

Top of a breakwater

Fig. 6.1.2-1 Description of Honma model
ΔH
q

H1

SeawallSea bottom

Fig. 6.1.2-2 Description of Aida model formula6.1.3 Execution of Numerical Simulation
6.1.3.1 Setting the Computational Region
It is important that the size of the tsunami source region, spatial waveform of the tsunami,
characteristics of the seafloor and coastal topography, structures and other such elements are taken
into account in the calculation region in a numerical simulation of a tsunami so as to appropriately
configure the calculation region so that the behavior of the tsunami, which includes refraction,reflection, diffraction, seiche, run-up and so on, is able to be calculated with good precision.

946.1.3.2 Setting the Grid Size
In numerical simulations of tsunami, a method is used to connect and simultaneously calculate
regions of the calculation grid size which differ depending on the spatial waveform of the tsunami or
topography conditions. In other words, the length of one wave of a tsunami spatial waveform in a sea
area is on an order between several kilometers to several hundred kilometers and the wavelength
becomes shorter as the water depth becomes less in coastal regions. Therefore, in line with this, a finer
grid size will be needed. In addition, because in many cases the topography of areas near the coastline
is intricate, the grid size needs to be appropriately configured in keeping with the scale of artificial
structures or the distinctive topography of the target coastline, in addition to the spatial waveform of
the tsunami.
The following points need to be kept in mind in configuring and connecting the grid sizes.
(1) Grid Size
Grid sizes are set as follows so that accurate calculation results can be obtained in each partial
region. However, what is shown below is a target value for the most general case where a numericalsimulation model is applied that is based upon the staggered grid and leapfrog difference method.
With respect to grid sizes and element dimensions in a case where the finite element method orother numerical simulation model is applied, the appropriate values need to be configured aftersufficiently examining the relationship between those and calculation error.
1) Tsunami Source Region
For the tsunami source region, the grid size is configured by focusing on the size of thetsunami source region and the spatial waveform of the tsunami.
As the criterion when configuring the grid size based on the spatial waveform of thetsunami, there is a method proposed by Hasegawa et al. (1987), which is a technique for
configuring 1/20 or less of one wavelength of the tsunami spatial waveform as the grid size.
2) Sea Area in Propagation Process
For a sea area in a propagation process, the grid size is configured by focusing on
refraction phenomena that have occurred due to the effect of submarine topography, in addition
to the tsunami spatial waveform.
In cases where the submarine topography is simple, the criterion when configuring thegrid size is the same as numeral 1), but there are also cases where the grid size is needed thatis 1/100 or less of one wavelength of the tsunami spatial waveform in regions where it isdetermined that the impact of refraction phenomena is great (see Section 4.3.2.1 of theappendix volume).
953) Sea Area around the Target Site
For sea areas around the target site, the grid sizes are configured by focusing on thetsunami spatial waveform, submarine slope inclination, sea floor and coastal topography, sizeand shape of seawalls and other structures.
In conditions where the coastal topography is not complex and there is almost no impact
from structures, the grid size from a depth of 50m or shallower to the shoreline is madegradually smaller from about 100m to 10m as the criterion.
In cases where there are ports or other such structures, it is known that, if a grid size thatis about 1/5 or less of the port opening width is used for the area around the port opening, then
the water level in the port will be able to be calculated with good precision (see Section 4.3.2.2of the appendix volume). Also, in cases where the area near the target site is a V-shaped port,
the grid size needs to be configured commensurate with ratio LV/λ between the port interiormean wavelength LV and the port length λ. In this case, there are also situations where when
LV/λ<6, a grid size needs to be 1/100 or less of one wavelength of an induced seiche or atsunami in the closed-off section of the port (see Section 4.3.2.2 of the appendix volume).
4) Land Area
For land areas under conditions where the topography is not complex, the grid size (Δx)
may be configured by means of the following equation which uses slope gradient α, cycle T,
and gravitational acceleration g (see Section 4.3.2.2 of the appendix volume).
x
 7  10  4 (Case where Manning’s coefficient of roughness2
gT
n=0.03m-1/3s)
x 4  10  4 (Case where friction not considered,gT 2
Goto and Shuto, 1983)(2) Connection of Regions with Different Grid Size
In numerical simulations of tsunami, the methods of connecting the regions with different
grid sizes according to the tsunami spatial waveform and topographic conditions are often used so
as to calculate these simultaneously (nesting). In such connection calculations, it is often the casethat the grid size is reduced to a ratio of 1/3 or 1/2 in order to alleviate the impact of part of theshort wavelength component that occurs in a small region, which does not propagate to a large
region and is re-reflected.
The computation may become unstable if the connecting boundary on the lateral side
intersects the coastline at an acute angle. This is because the reflected wave from the coastline
reaches the lateral side boundary immediately; further, the difference between the actual and96

calculated results for a region with a larger grid size is large when the numerical results are
obtained for an outer region with a rough topography. It is desirable to take such cases into accountin configuring connection regions so that the lateral connection boundaries and land coastline do
not intersect at acute angles.
6.1.3.3 Preparation of Topographic Data
(1) Sea Area Topographic Data
The technology for measuring water depth distribution has dramatically improved thanks to
the development in recent years of sonic depth finding technology and satellite position measuring
technology covering a broad range. For this reason, in numerical simulations of tsunami, it isdesirable that the water depth data is prepared based on the latest measurement results from thestandpoint of improved accuracy.
For the sea area topographic data, the bathymetric digital data and other information presented
in Section 3.2 of the main volume may be utilized. Also, soundings and other specific measurement
data may also be used after verifying such accuracy.
(2) Land Area Topographic Data
It is also desirable that land area topographic data are prepared based on the latest topographic
maps and other such sources, and the material presented in Section 3.2 of the main volume may
be utilized as land area topographic data. Also, specific measurement data may be utilized after
verifying such accuracy.
(3) Data of Past Topography
In case where artificial modifications (erection of structures, land reclamation, etc.) that did
not exist at the time of the past tsunami incident is reflected in the latest topographic data, whencomparing the run-up height of past tsunami at the target site with the tsunami height or
reproducing the past tsunami heightat the time of simulation, it is possible to utilize topographic

data such as the ancient map shown in Section 3.2 of the main volume in which the topography
before modification is described.
6.1.3.4 Preparation of Structure Data
(1) Buildings or Other Structures and Two-Dimensional Structures (Linear Structures)
Structures such as buildings that exist in the process of tsunami propagation and run-up, andtwo-dimensional structures such as sea embankments and breakwaters may affect the behavior of
the tsunami. Two-dimensional structures, in particular, need to be given sufficient attention in the97preparation of structure data due to their comparatively large impact, such as obstructing thetsunami flow or changing its direction. Two-dimensional structures include sea embankments, tideembankments, breakwaters, and river levees.
In tsunami calculations, there are many cases where these structures are treated as described
below commensurate according to the size of the structure.
1) Cases Where Structures Treated as Topographic Data
In cases of sea embankments, breakwaters and other two-dimensional structures where
the width of the structure is wider than the grid size, the height of the structure is assumed in
the grid and treated as topographic data.
2) Cases Where Structures Treated as Overflow Boundary Conditions
In cases of sea embankments, breakwaters and other two-dimensional structures where
the width of the structure is narrower than the grid size, the structure is arranged as if there isa wall in between grids and the height is taken into account in overflow boundary conditions.
3) Cases Where Structures Addressed by Combining Topographic Data and Overflow Boundary
Conditions
In cases where a parapet or other structure, which has a narrow width, has been erected
on a breakwaters or other structure that has a wider width than the grid size, the structure may
also be addressed by combining 1) topographic data and 2) overflow boundary conditions.
4) Cases Where Structures Treated as if No Structure Present
Detached breakwaters and other such permeable structures for which wave-dissipatingconcrete blocks have been stacked up are in many cases treated as though there is no structure
present at all.
(2) Consideration of Earthquake Resistance and Tsunami Resistance
Because the tsunami often comes after the earthquake, it may be necessary to consider thesituation after the earthquake depending on the earthquake resistance of the structure. Also, withembankments and other such structures, scouring may also be anticipated when the tsunami
overflows, so there are also cases where scouring of such structures is reflected in numericalsimulations as necessary.
(3) Gates, Curtain Walls and Other Structures with Underwater Openings
In cases where there are gates, curtain walls or other structures with openings underwater,these are modeled by using a method capable of appropriately computing the flow rate through the
opening, as necessary. The calculation formula set forth by Kuriki et al. (1996), which is shown98

below, is a method for calculating this pass-through flow rate.
In cases where the tsunami exceeds the crown of a gate or curtain wall, the overflow volume,
which is determined based upon Honma (1940) presented in Section 6.1.2.3 of the main volume,is added to the flow rate passing through this opening.
Table 6.1.3-1 Calculation formula for pass-through flow rate for structures having an opening
underwater (Kuriki et al., 1996)
Water level relationshipCalculation formula

Flow rate coefficient C

Free outflow :
i

h1 

3
H
2

h1 

3
H
2

h2  Hii

iii

h2  HQ  CBh2 2 g ( h1  h2 )However, in case of3h1
2
 , then h2  h1
3
2
h2

0.79

Intermediate outflow :Q  CBH 2 gh 1

0.51

Submerged outflow :Q  CBH 2 g ( h1  h2 )

0.75

上流側

下流側
h 1h1

h2h 2

HＨ

Q
Q

h1, h2: Water level in facility (m), H: Opening height (m), Q: Flow rate (m3/s),
B: Opening width (m), C: Flow rate coefficient, g: Gravitational acceleration (m/s2)
Figure 6.1.3-1 Diagram of calculation formula proposed by Kuriki et al. (1996)

99

6.1.3.5 Setting Various Coefficients, etc.
(1) Coefficients Relating to Friction term
Coefficients assigned to friction term may be configured with reference to the literature andother sources indicated in Table 6.1.3-2.
Table 6.1.3-2 Coefficients assigned to friction term
Name ofcoefficientManning’s
coefficient ofroughness n(m-1/3s)

Frictioncoefficient kb

Values presented in literature
Iwasaki and Mano (1979): Sea area 0.03
Goto and Sato (1993): Sea area 0.025
Kotani et al. (1998): Run-up area(As given below)
High-density residential area: 0.08
Medium-density residential
area: 0.06
Low-density residential area: 0.04
Forest area: 0.03
Rice/vegetable fields: 0.02
Tanaka (1985): Deep sea area: 0.0026
Shallow sea area: 0.005 to 0.01
Run-up area: 0.01 ~ 0.5

Values often utilized in assessmentsof tsunami water levels for design of
nuclear power plants
Sea areas: 0.025, 0.03
Run-up area: 0.025, 0.03
Run-up area near the target site:
Configured in accordance with the
topography

Deep sea area
: (15m or deeper): 0.0026
Shallow sea area
: (15m or shallower): 0.00637
Run-up area: 0.01

However, in cases where the friction coefficient is modified according to the water depth, it
is desirable that it be configured so that it changes smoothly because there are also cases where
the results of calculation of the velocity field at such location becomes unnatural when a change
is made in a discontinuous manner.
(2) Horizontal Eddy Viscosity Coefficient
If the horizontal eddy viscosity coefficient is 10m2/s (105cm2/s) or less, then the rate of waterlevel decline will be about 5% or less in comparison to a zero case (see Section 4.3.3.2 of theappendix volume), so in cases where a change in the water level is subject to assessment, 10m2/s(105cm2/s) may be set as the criterion for the maximum value.
With the Tanaka method, 10m2/s (105cm2/s) has been empirically adopted as the horizontal
eddy viscosity coefficient.

100

(3) Wave Depth Relating to Tsunami HeadIn theory, when the water depth at the tsunami head becomes zero, that location turns into a
newly exposed area. However, in actuality, there are cases where meaningless calculations arecontinued at minute water depths caused by numerical simulation error. Also, because water depthof the run-up tsunami head is very small, denominators for friction and advection term become
smaller and numerical simulation becomes easy to diverge.
Therefore, the two methods are used. The first method sets "Minimum water depth" so as not
to carry out calculation by regarding the water depth at the tip as zero, and the second method sets
"Virtual water depth" so as not to make the water depth, which is substituted for the friction term
and advection term, smaller than a certain water depth. Imazu et al. (1996) conducted research on
minimum water depth and virtual water depth, and this study may be referenced in such setting.
6.1.3.6 Setting Simulation Time and Computation Time Interval(1) Simulation TimeThe first wave of a tsunami is not always the largest, and the time when the largest wave riseschanges depending on the initial water level of the tsunami, topographic conditions near the target
site and other factors. For example, in cases where the resonant oscillation inside the bay are
excited and cases where reflective waves and succeeding waves overlap, the maximum water level
may also occur after several waves, and it is important to set a sufficient simulation time to grasp
these.
(2) Setting Computation Time Interval
For grid size appropriately set according to the concept described in Section 6.1.3.2 of themain volume, computation time intervals are set to satisfy the Courant-Friedrichs-Lewy (CFL)
condition (a general condition of stability in numerical simulations of wave motion, and, theconditions for cases of plane two-dimensional numerical simulation are indicated below) shown
below, taking account of the stability of the simulation.
x
2 ghmax

t 

where, x: Grid sizet : Computation time interval
hm ax : Maximum water depthg: Gravitational acceleration.

Ordinarily, calculation regions with different mesh sizes are connected and the numericalsimulation is carried out all together with the time intervals set to be constant. Firstly, t is found101

so that the CFL condition is satisfied for each region where x is the same, and, finally, theminimum t or less is adopted as the computation time interval.
However, in cases where actual calculations are performed, numerical error and nonlinearityof phenomena interfere, so t needs to be configured smaller with some margin in comparison
to  x

2 gh max . In particular, when performing calculations in a case where high velocity flow

is present in coastal or other such areas where the inundation depth become smaller, there are also
cases where the flow velocity value will become greater than tsunami propagation velocity
gh max and this leads to calculation divergence.

6.1.4 Three-Dimensional Model
6.1.4.1 Basic Approach
Three-dimensional models may be used as a useful means when reproducing the threedimensional flow of a tsunami around a structure or other such location, and when assessing thetsunami wave force more precision. However, tremendous computational resources are necessary toeffectuate all three processes of tsunami occurrence, ocean propagation and land run-up in a threedimensional model. Accordingly, it is necessary to devise measures such as limitation of calculation
region, appropriate configuration of reproduction time of phenomenon, proper coupling with planetwo-dimensional model, etc.
6.1.4.2 Typical Three-Dimensional ModelIn the application of a three-dimensional model, it is desirable to use an analysis code that has
been verified for assessment of tsunami wave force and three-dimensional fluid behavior having awater surface. An overview of typical three-dimensional fluid analysis codes and case studies verifying
their validity are given in Table 6.1.4-1.
6.1.4.3 Perform of Numerical Simulation
Ordinarily, calculation grid sizes in a horizontal direction of a three-dimensional model need tobe made even smaller than those of a plane two-dimensional model. Also, there are cases where thecalculation accuracy of the hydraulic quantity decreases when the calculation grid sizes in a verticaldirection are rough. Nevertheless, a well-defined index for grid division of three-dimensional models
has not been proposed as of the current point in time, so it is desirable to verify that appropriate
calculation accuracy is able to be obtained in comparison with proven analysis results and hydraulic102

model experiment results by performing preliminary calculations or other such techniques.
Case studies of analyses of hydraulic model experiments, which are given in Section 4.1.6 of theappendix volume, may be referenced with respect to verifying the validity of three-dimensionalmodels.
Table 6.1.4-1(1) Previous case studies of typical three-dimensional fluid analysis codes
Name ofCase study verifying
analysis code
Summary
validity(source)
CADMAS・ Non-hydrostatic three-dimensional model for Validity was verified
SURF/3D
which the governing equation is continuity based on aequation and the Navier-Stokes equation enhanced comparison with the(Coastalfor porous model, which focus on three- results of model
Development
experiments on rundimensional incompressible viscous fluid.
Institute of・ For discretization over time, the Euler method, up tsunami withTechnology,
coupling of the momentum equation is used, and respect to fluid
2010)
the SMAC*1 method is used for continuity behavior and wave
equation, and the VOF*2 method is used for the pressure (Arikawa etal., 2005)
free surface analysis model.
・ In addition to calculations of wave pressure andbehavior of tsunami running up on land, couplingis also possible with gas, ground and solids.
OpenFOAM・ Analysis code for two-phase flow of immiscible Verified by applying
fluid incompression of water and air (interFoam OpenFOAM(OpenFOAM
calculations forsolver).
Foundation)
・ Using the continuity equation and Navier-Stokes reproducing waterequation for incompressible fluids as the column collapse
governing equation, the finite volume method is issues and run-up
employed to perform discretization and the PISO*3 tsunami hydraulicmethod is used to calculate flow velocity and experiments, andcompared with thepressure.
・ The VOF method is used for tracking gas-liquid results of tests on
fluid behavior andinterface.
・ Tsunami behavior along the coastline, including water pressure (Phamet al., 2012;
run-up tsunami, may be calculated.
Kawasaki et al.,
2013)

103

Table 6.1.4-1(2) Previous case studies of typical three-dimensional fluid analysis codes
Name of analysis
code (source)

Summary

Storm Surge and ・ Hybrid model capable of connecting, as necessary,
Tsunamithe quasi-three-dimensional hydrostatic multilevel
Simulator
model STOC-ML with the three-dimensional non(STOC*4)hydrostatic flow model STOC-IC.
・ Capable of analyzing propagation and run-up of far(Tomita andfield tsunami and near-field tsunami, soliton fission,
Kakinuma, 2005;
interference with structures, and tsunami debris.
Takahashi andSTOC-ICTomita, 2013)
・ Non-hydrostatic three-dimensional model, whichuses as its governing equation the Reynolds
equation and continuity equation applying the
porous model to discretize space over a staggeredmesh and uses the leapfrog method to evolve overtime.
・ Correspondingly applies the time evolution-typebore model to the wave breaking model.
STOC-ML・ Calculation may also be performed in single layers
using a quasi-three-dimensional model that divides
the calculation region into multiple phases in a
vertical direction and assumes hydrostatic pressure
at each phase.
・ Other than the fact that pressure is not solved andwave breaking is not taken into consideration, it is
the same as STOC-IC.
DOLPHIN-3D・ Three-dimensional multiphase flow turbulence
numerical model which is based on the expanded(Kawasaki and
SMAC method and CIP*6 method which adopts
Hakamada,
irregular interval grids, kinematic analysis
2007)
techniques for multiple rigid bodies, and the
dynamic bivariate mixing model DTM*5.
・ The governing equation is comprised of a massconservation method for compressible viscous fluid,
momentum equation, pressure equation, advection
equation with density function indicating theinterphase ratio, and equation of state for barotropic
fluid.
・ The behavior of run-up tsunami and other suchwaves, interaction between structures and tsunami,
and the dynamic behavior of tsunami debris are able
to be calculated.

104

Case study verifying
validity
Model validity andprecision has beenverified based on acomparison withmodel experimentsof tsunami on
inclined planes,
experiments on
overflow ofrectangular weirs,model experiments
on tsunami
breakwaters, andmodel experiments
based on actual
topography (Tomita
and Kakinuma,
2005; Tomita andHonda, 2008;
Takahashi andTomita, 2013)

Verified in acomparison withresults of modelexperiments on
collisions anddrifting ofrectangular rigid
bodies with bore
following watercolumn collapse
with respect to fluid
behavior and wave
pressure (Kawasaki
et al., 2006;
Kawasaki and
Hakamada, 2007)

Table 6.1.4-1(3) Previous case studies of typical three-dimensional fluid analysis codes
Name ofanalysis code(source)
Tsunamicomplexdisaster
forecasting
model(Yoneyama andNagashima,
2009)

Summary・・・
C-HYDRO3D

・

Kihara andMatsuyama,
2010; Kihara etal., 2013;
Kihara et al.,
2012)
・

・

・

Case study
verifying validity

Non-hydrostatic three-dimensional model for The validity of runincompressible fluid in which the VOF method is up tsunami andused for predicting surface behavior and the tsunami debris
FAVOR*7 method is used for handling boundary behavior have beenvalidated based on a
profiles.
The governing equation is comprised of the comparison with thecontinuity equation, the Reynolds equation, results of model
advection equation for fluid volume and the turbulent experiments
flow valuation formula, and these are discretized on (Yoneyama et al.,an orthogonal coordinate system and analyzed based 2008; Yoneyama
and Nagashima,on the SIMPLE*8 method.
In addition to fluid movement, vessel movement and 2009)
mooring line tension may also be calculated.
Three-dimensional
numerical
model
where ・ Validatedhydrostatic approximation is assumed in which
reproducibility ofpartial continuity equation based on topographic
tsunami behavior
frame of reference, continuity equation that isand geomorphic
vertically integrated from subgrade to water surface,change for theand a momentum equation with a horizontal direction
area around ports
in which hydrostatic approximation used are used asin Sri Lanka using
the basic equations.
model
experiments and
For the turbulence model, the Mellor and Yamada
the 2004 Sumatra
level 2 model has been adopted for the verticalearthquake
direction and the Smagorinsky model for thetsunamihorizontal direction.
The finite difference method is used for ・ Using acomparison withdiscretization, a staggered arrangement formoving-bed open
arrangement of variables, and the FSC method,channelwhich is a semi-implicit method, for time evolution
experiments,of the governing equation.
verticalIn addition to calculating tsunami propagation from
distribution of
the tsunami source region to the coastline as well as
suspended
overflow and the run-up flow, calculations may also
sediment
be made of geomorphic change due to the tsunami
concentrations
and the movement of tsunami debris.
has been validated(Kihara andMatsuyama, 2010;
Kihara et al.,2012)

*1 SMAC: Simplified Marker and Cell
*2 VOF: Volume of Fluid*3 PISO: Pressure-Implicit with Splitting of Operators*4 STOC: Storm Surge and Tsunami Simulator in Oceans and Costal Areas*5 DTM: Dynamic Two-parameter mixed model105

*6 CIP: Cubic Interpolated Propagation*7 FAVOR: Fractional Area/Volume Obstacle Representation*8 SIMPLE: Semi-Implicit Method for Pressure-Linked Equation
6.2 Numerical Methods for Tsunami Generated by Submarine Landslides, Slope Failure, Flank
Collapse, etc.
6.2.1 Basic Approach
There are several triggers for generation of tsunami: submarine landslide, slope failure, flankcollapse caused by volcanic activity or other such events (hereinafter, referred to as “landslides, etc”.).
In the numerical simulations of tsunami we should take into account the requirements foritspropagation and run-up calculations described in Section 6.1 of the main volume. It is particularly
necessary to keep these requirements in mind in determining computational conditions and modelingthe process of tsunami generation.
6.2.2 Selection of Numerical Model
Although various numerical methods have been proposed with respect to tsunami due tolandslides, etc., there are few cases of such application in comparison with tsunami occurring due tofault movement. For this reason, in selecting a method, attention needs to be given to phenomena
anticipated by each method and the scope of such application.
Considering uncertainty with the numerical method, it is conceivable that multiple methods may
be selected and applied to anticipated phenomena. The selection of a method and the validity of theconfiguration need to be verified by, for example, comparing multiple calculation results against eachother.
Table 6.2.2-1 shows numerical simulation methods for tsunami due to landslides, etc. The methods
are described in Section 4.4.1 of the appendix volume.
6.2.3 Execution of Numerical Simulation
6.2.3.1 Setting the Computational Region and Grid Size
Based on the spatial waveform of the tsunami, characteristics of the topography from the tsunami
source to the evaluation points and other elements, computational region and grid size areappropriately determined as with tsunami due to fault movements. In tsunami source regions where106landslides and other such events may occur, considering the size of the depletion zone andaccumulation zone as well as the wavelength of the tsunami, we need to determine an appropriate gridsize. For example, with the Kinematic Landslide model where the distribution profile and movementof landslide bodies are input and the two-layer flow model where the initial distribution profile oflandslide bodies is input and the subsequent distribution and movement can be calculated, in cases
where a model the distribution profile and movement of landslide bodies are input and calculated isutilized, a computational region is configured so that the region comprising movement of landslide
bodies that give rise to tsunami (=tsunami source region) is included, and then a grid interval needs tobe configured that is appropriate for representing the distribution profile and movement of landslide
bodies.
Reference information concerning grid intervals appropriate for tsunami source regions is given
in Section 4.4.2 of the appendix volume.
6.2.3.2 Setting the Computation Time Interval
In determining computation time interval, in addition to satisfying the CFL condition, it isnecessary to satisfy the conditions that accord with the selected numerical simulation model for theprocess of tsunami generation. However, there are few methods for which the conditions forcomputation time interval are clearly defined and, moreover, numerical error, nonlinearity, and otherissues are involved, so a determination needs to be made on verifying validity and convergence as towhether or not the computation time interval has been appropriately set for the actual calculation.
6.2.3.3 Topographic Conditions
As for input conditions for numerical simulation of tsunami due to landslides, etc., there are cases
where it is necessary to have topographic conditions for landslides, etc. such as the disintegrated
sediment volume, topography before and after collapse, and topography of slip planes. With respect
to landslides, etc. that generated in the past, Hiraishi et al. (2001) (submarine landslides) and Satake
and Kato (2001) (flank collapse) provide case studies that reconstruct the pre-occurrence topography
based upon data about the topography in the vicinity of the generation area. The Express Highway
Research Foundation of Japan (1985) offers a method for preparing the collapsed surface of a slope
failure. Also, reference for configuring topographic conditions have been describedin Section 3.3.1 ofthe main volume.

107

6.2.3.4 Various Coefficients, etc.
Various coefficients and other constants need to be appropriately determined on the basis of thenumerical method and the phenomena. Values of various coefficients from previous studies are given
in Section 4.4.1 of the appendix volume. Also, with respect to several numerical methods, studies of
the relationship between simulation conditions and computed tsunami heights are given in Section
4.4.3 of the appendix volume.
Many previous studies have determined coefficients through a process of trial and error bycomparing calculation results and the run-up height of past tsunami. In the determination of various
coefficients, the characteristics of events need to be taken into account in examining the difference
between the values considered while, at the same time, continuing to reference setting values for which
reproducibility has been verified in past reviews. In determining the various coefficients related totopography after landslides and landslide movements, it is considered effective to reference the resultsof analyses based on models used for analyzing landslide movement (LSFLOW, TITAN2D, FLOW3D,
etc.). For example, Sasahara (2004) used LSFLOW to perform a flank collapse simulation and verify
consistency by comparing the results interpreted from submarine topography maps and calculation
results with respect to the range of distribution of collapse sediment.

108

Table 6.2.2-1(1) Numerical models for tsunami occurring due to landslides, etc.
Name of model
Flow rate model

Circular slip
methodKinematic
Landslide model

Landslidemovement
analysis model

Summary

Input conditions

Examples of application

Method to give the inflow Volume of depleted Numerical Experimentsof depleted mass into the mass, position and width oftheTsunamisea as the seawater flow of coastline to which Associated with therate along the coastline
depleted mass flows CollapseofMt.
into, duration of inflow, Mayuyama in 1792
etc.
(Aida,
1975),
andTsunamis Generated by
Eruptionsfrom
Komagatame Volcano,
Hokkaido,
Japan(Nishimura and Shimizu,
1993)
Method to give the Landslide
profile 1771 Meiwa Yaeyama
topography before and after topography,
landslide (Hiraishi et al., 2001)
landslides on unstable volume magnification
slopes derived using the factor,
landslidecircular slip method and duration, etc.
reflect this in the sea
surface water level
Method to find the Topography before and 1741 Oshima-Oshima
submarine
geomorphic afterlandslide, flank collapse (Satakechange based on the movement velocity of andKato,2002),
topography before and after the landslide, duration of Volcanic origin of thelandslide,movement landslide, etc.
1741 Oshima-Oshima
velocity of the landslide,tsunami in the Japan Sea
and duration of the(Satake,2007)andlandslide and give this in asubmarine landslides offtime series as sea surface
Oahu Island (Satake etchangeal., 2002)
Method to give the change Initial depleted mass Numerical Simulation of
in bed thickness of depleted distribution, coefficients the Tsunami caused by
mass, which is obtained by necessary for landslide the sector Collapse ofusing an analytical model kinematic
analysis Mt.
Mayuyama,(for example, LSFLOW, (friction angle of slip Shimabara
Peninsula,
TITAN2D or FLOW3D) to plane,
densityand Kyushu
in
1792
solve
for
landslide viscosity coefficient for (Sasahara, 2004)
movement, in a time series depleted mass, etc.), etc.
as sea surface change

109

Table 6.2.2-1(2) Numerical models for tsunami occurring due to landslides, etc.
Name of model

Summary

Input conditions

Two-layer flow
modelsubmarine
mass failure

Examples of application

Method to solve a shallow Initial sediment bed 1998 Papua New Guinea
water equation with two thickness distribution, submarine
landslides
verticallayerswhere sedimentdensity, (Hashi and Imamura,sediment is the bottom various
coefficients 2000), and Model oflayer and seawater is the relating to inter-layer tsunami generation by
upper layer by taking into interaction (coefficient collapse of volcanic
consideration
the of interfacial resistance eruption:
the
1741interaction between layers force, etc.), etc.
Oshima-Oshima
tsunami, in Tsunamis:
Case Studies and Recent
Developments(Kawamata et al., 2005),
etc.(However, only theprediction equation for
maximum amplitude has
been verified based on acomparison with pasttsunami)Predictive
Method to estimate the Characteristic values of Tsunami Generation byempirical
initialwaterlevel the landslide topography Submarine Mass Failure.
equationsdistribution by combining (length,
thickness, II: Predictive Equations
describing tsunami an equation that gives the width,etc.), and Case Studies (Watts
generation byplane
two-dimensional characteristic values of et al., 2005)
submarine mass
distribution of tsunami the tsunami source (However, only the
failure by Watts et water level and a prediction region (water depth, prediction equation foral. (2005)
equation that gives the slope gradient, etc.), etc. maximum amplitude has
been verified based on a
maximum amplitude andcomparison with past
wavelength of tsunami intsunami)the tsunami source region
for submarine landslides
Distinct element
Method where a two-phase Physical properties of Reproduction of water
methodflow model that treats solid solid phase particles tank experiments (Gotophase with the distinct (particle size, resistance et al., 2011)
element method and fluid coefficient, porosity ofresistanceforce
as particle fluidized bed),interaction in coupling with andthephysical
fluid
phase
(particle properties
offluid
method) is used(density,
viscosity
coefficient)1106.3 Water Level Fluctuation Simulation of Sea Water Intake and Discharge Facilities
6.3.1 Basic Approach(1) Purpose of Simulation
Of the risks anticipated when a tsunami reaches a nuclear power plant, the risks relating to
sea water intake and discharge facilities include inundation from above such a facility due to therise of the water level within the sea water intake and discharge facilities, and inundation of pump
motors, and impossibility of water intake due to lowering of the water level of water tank, etc.
(Figure 6.3.1-1). In order to examine the impact that these risks have on a nuclear power plant, itis necessary to ascertain the degree of water level fluctuation within the facility, but there are also
cases where the water level fluctuation within the facility is amplified when components areincluded that are the same degree as the eigen period for the target facilities in the waveform of
the tsunami arriving at the water intake or discharge. Accordingly, in cases where it is conceivablethat a tsunami will cause the water level within a sea water intake and discharge facilities tofluctuate, it is necessary to simulate the water level fluctuation within the sea water intake anddischarge facilities.
If it is obvious that the target site is not affected by the tsunami (eg, the amplitude of thetsunami at the water intake or discharge position is small and there is a large difference in the
predominant period of the target tsunami and the eigen period of the facility, it is possible to omit
simulating the change in the water level at the corresponding water discharge facilities.
(2) Selection of Numerical Simulation Method
The method for simulating fluctuation in the water level due to tsunami for water intake
facilities (intake - intake channel - intake tank) and discharge facilities (discharge tank - discharge
channel - discharge) is generally performed using the calculation tsunami waveform at the water
intake or discharge as the water level boundary condition. The flow within the water intake anddischarge channels may be treated as a one-dimensional flow along a water channel, and, in cases
where there is only open channel flow, cases where there is only pipeline flow (flow in acompletely filled state without a free water surface), and, moreover, cases where both of thesesituations coexist, an appropriate basic equation and simulation method are applied which areable to simulate these with good precision.

111

(3) Modeling of Sea Water Intake and Discharge Facilities and Implementation of Numerical
Simulation
In performing the water level fluctuation simulation for a sea water intake and discharge
facilities, the eigen period of the tsunami which is an external force and the hydraulic response
characteristics (eigen period) of the sea water intake and discharge facilities overlap, and it resultsin the cases where fluctuation in the water level of the water intake and water discharge tanks is
amplified, so it is important that the sea water intake and discharge facilities be modeled with goodprecision.
In modeling a sea water intake and discharge facilities, the water channel flow path length
and water flow cross-section, water tank shape and other such elements be configured based on
structural diagrams of the facility and other such sources, and the water channel friction loss andshape loss (refraction, bending, etc.) as well as facility internal structures (screens, overflow weirs,etc.) are appropriately configured.
Also, with respect to the impact of shells and other marine organisms attaching to wall
surfaces, it is desirable that such effects be appropriately reflected in keeping with the assessment
object. In addition, because there is the possibility that water intake or discharge volume, tideconditions, and crustal movements from earthquakes may also have an impact on the hydraulicresponse characteristics or other such attributes, these are included as simulating conditions asnecessary.

Figure 6.3.1-1 Overview of water level fluctuation simulation and risks related to sea water intake anddischarge facilities1126.3.2 Selection of Numerical Simulation Method
6.3.2.1 Simulation Methods for Water Channel Portion
The flow through the water channel portion is classified depending on the water channel structureand fluctuation in the water level when a tsunami strikes into (1) cases where all sections are pipeline
flow (flow in a completely filled state), (2) cases where all sections are open channel flow, and (3)cases where there are both sections with an open channel flow and sections with a pipeline flow
(section in a completely filled state), and the simulation method applicable to the respective flow
situation needs to be selected.
(1) Cases Where All Sections Are Pipeline Flow
In cases where the water channel portion has a pipeline flow through all sections (flow in acompletely filled state), a free water surface does not develop within the water channel, so theintake (or discharge) water level and the intake tank (or discharge tank) water level serve as theboundary conditions, and an equation for one-dimensional unsteady flow through the pipeline may
be used to simulate the flow rate through the water channel section. The intake tank (or dischargetank) water level is sequentially simulated using the calculated flow rate for the water channel
section in the previous step (see Section 6.3.2.2 of main volume).
(2) Cases Where All Sections Are Open Channel Flow
In cases where all sections are open channel flow, either of the following simulation methods
is often used.
・

Method of applying an equation for one-dimensional unsteady flow through an open
channel used in simulation of river flood flow and other such situations

・

Method of modeling the water channel using a plane two-dimensional grid and applying
nonlinear long-wave theory or other such scheme(3) Cases of Both Sections with Open Channel Flow and Sections with Pipeline Flow
In cases where there are both sections with an open channel flow and sections with a pipeline
flow (section in a completely filled state) within a water channel, either of the following two
simulation methods is often used.
・

Simulation method based on the slot model
As shown in Figure 6.3.2-1, the slot model (for example, Ohtani et al., 1998) is able toconfigure a virtual slot above a pipe so that the pipeline section may also be treated as open
channel flow. Accordingly, it is no longer necessary to distinguish between open channel
113sections and pipeline sections and the method is applied to an equation for one-dimensional
unsteady flow through an open channel in all sections. The slot width is configured
dependent upon the pipeline cross-section and pressure wave velocity (about 100m/s).
Virtual slot

Bs

Slot width

where,gA
Bs  max
c2

Amax ：Pipeline cross section

c 100m/s

Amax

Open channelc ：Pressure wave velocity

g ：Gravitational Acceleration

Pipeline

Figure 6.3.2-1 Overview of slot model・

Simulation Method Separating Open Channel Section and Pipeline Section
As shown in Figure 6.3.2-2, each portion of the water channel separated into minutesections is sequentially assessed to determine whether it is in an open channel state or apipeline state, and the flow rate for the pipeline sections is simulated by using the water levelof the open channel sections at both ends (water level of the free water surface) as theboundary conditions (in the pipeline sections, the wave velocity of the pressure wave isassumed to be infinity, and the cross-section flow rate within the pipeline section is regarded
as the same). Just as with the slot model, an equation for one-dimensional unsteady flow inthe open channel is applied to the open channel sections.

Figure 6.3.2-2 Overview of simulation method separating open channel section and pipeline section
6.3.2.2 Simulation Method for Water Intake/Discharge Tanks and Pits
For intake and discharge tanks as well as pits (hereinafter, these are collectively referred to as“water tanks”), the appropriate simulation method is to be selected from among the methods indicated114below in accordance with the simulating conditions and shape of the water tank to be modeled. In allof these methods, the flow rate through the water channel connecting to the water tank is used as theboundary condition, and the water level and flow velocity inside the water tank, volume of overflow
from upper part of opening on water tank are computed. However, the computed water level of thewater tank interior is used for computing the flow rate of the water channel portion in the next step, so
all of these methods also need to be treated as issues coupled with the water channel portion.
・

Simulation method based on model taking into consideration only change in water volume
within the water tankThis method is used with the relationship between water level and volume that
integrates the water surface area in the water tank interior in a vertical direction so as tocompute the water volume and water level within the water tank based upon the total flowrate value for water channels connected to the water tank.

・

Simulation method based on one-dimensional water channel modelThis method models the water tank interior using an open channel and then utilizes a
one-dimensional unsteady flow continuity equation and momentum equation to compute thewater level and flow rate of the flow direction inside the water tank.

・

Simulation method based on plane two-dimensional modelThis method is similar to the numerical model used in plane two-dimensional tsunami
simulations. The method models the water tank interior using a plane two-dimensional gridso as to compute the water level and flow velocity distribution within the water tank using
the nonlinear long-wave theory or other such scheme.

・Simulation method based on three-dimensional modelThis method models the water tank interior using a three-dimensional grid (structured
grid or non-structured grid) so as to compute the water level, pressure and flow velocity
inside the water tank three-dimensionally.

6.3.3 Modeling of Sea Water Intake and Discharge Facilities and Implementation of Numerical
Simulation(1) Modeling of Sea Water Intake and Discharge Facilities
Sea water intake and discharge facilities are modeled based on the specifications taken below
from structural diagrams and other such drawings.
・

Water channel portion: water channel elevation, water channel inclination, water channel length, water channel
cross-section profile, etc.

・Water tank portion115

: cross-section profile of ponding area, water surface area or water volume according toheight, height of overflow from upper part of water tank, etc.
When simulating fluctuation in the water level of a sea water intake and discharge facilities,
the modeled water channel portion and water tank portion are connected and, ordinarily, thesimulation is made comprehensively for the entire system.
The events subject to assessment in the simulation of fluctuation in the water level of a sea
water intake and discharge facilities are the lowering of the water level at the location where thewater intake pump is installed, overflow from above the water tank, and other events. Along with
this, it is necessary to compute the water level fluctuation at the assessment point, and the hydraulicresponse characteristics (eigen period) of the sea water intake and discharge facilities come to beclosely involved in the magnitude of the water level fluctuation. In cases where loss is disregarded
with a single water channel and simple structure in the intake tank, the eigen period for the facility
with a pipeline flow (all sections in a completely filled state) is expressed below (see for example,
Tsubaki, 1974).

T  2

AL
gawhere, T: Eigen period (s), A: Water tank plane area (m2), a: Completely filled pipe cross section(m2), L: Water channel length of completely filled section (m), g: Gravitational Acceleration (m/s2).
In a case where the eigen period of the facility and the predominant period of the tsunami
input at the water intake or discharge are at the same degree, the water level fluctuation within thefacility is amplified. Also, in cases where a pump bearing slab or other such component is installed
within the water tank or other such cases involving a structure where there are sudden changes in
the water surface area of the water tank, the eigen period of the facility will also fluctuate according
to the water level, so the structure may also become the factors which amplify water level
fluctuation. Accordingly, it is important that an appropriate model be constructed based on
structural diagrams and other such information about the facility.
(2) Application of Water Channel Friction Loss and Shape Loss
Ordinarily, Manning’s law is applied to friction loss in water intake channels and water
discharge channels. The friction loss of head, which is based on Manning’s law, is expressed using
the following equation (Electric Power Civil Engineering Association Compilation, 1995).

h f  n 2 V 2

L
R4/3

where, hf: Friction loss of head (m), n: Manning’s coefficient of roughness (m-1/3s), V: Crosssection flow velocity (m/s), L: Water channel length (m), R: Hydraulic radius (m).
Tables 6.3.3-1, 6.3.3-2 and 6.3.3-3 show examples of configurations of Manning’s coefficient116

of roughness and the thickness of shellfish adhesion along water intake channels as given by theElectric Power Civil Engineering Association Compilation (1995) (Figure 6.3.3-1 is presented as
reference material for water intake and discharge channel profiles in Table 6.3.3-1 and Table 6.3.32). These need to be appropriately configured in accordance with the assessment target.
The formulas presented in the Electric Power Civil Engineering Association Compilation(1995), Japan Society of Civil Engineers Compilation (1999) and other sources are applied tocurvature, refraction and other shape loss, and simulations are necessary that appropriately modelsuch shape loss in the numerical simulations as well.

Table 6.3.3-1 Thickness of shellfish adhesions, etc. on intake channel and coefficient of roughness(Electric Power Civil Engineering Association Compilation, 1995)
Type of water intake
Cross-section flow
Thickness of shellfish
Coefficient ofchannelvelocityadhesions, etc.
roughness
0 ~ 20cm
0.014 ~ 0.027
Culvert
0.8 ~ 2.2 m/s(Often 0, 5 or 10cm)(Often 0.015, 0.020)
Pipeline

2.0 ~ 3.6 m/s

0 ~ 10cm

0.015 ~ 0.018

Table 6.3.3-2 Thickness of shellfish adhesions, etc. on discharge channel and coefficient of roughness(Electric Power Civil Engineering Association Compilation, 1995)
Type of water
Cross-section flow
Thickness of shellfish
Coefficient ofdischarge channel
velocityadhesions, etc.
roughness
0 ~ 20cm
Culvert
1.6 ~ 3.6 m/s
0.014 ~ 0.027(Often 0cm)
0 ~ 20cm
Tunnel
1.8 ~ 3.0 m/s
0.014 ~ 0.027(Often 0cm)

Open channel

Pipeline

CulvertFigure 6.3.3-1 Examples of types of intake and discharge channel structures(Electric Power Civil Engineering Association Compilation, 1995)

117

TunnelTable 6.3.3-3 Manning’s coefficient of roughness n(Electric Power Civil Engineering Association Compilation, 1995)
Range of nMaterial
Good concrete lined water channel constructed using steel form

0.011 ~ 0.014

Ordinary concrete lined water channel

0.012 ~ 0.016

Unlined tunnel with only poured concrete foundation

0.020 ~ 0.030

Total cross-section unlined tunnel

0.030 ~ 0.040

Welded steel pipe

0.010 ~ 0.014

Revit connection pipe

0.013 ~ 0.017

Ordinary concrete water channel with shellfish adhesion

0.017 ~ 0.020(3) Treatment of Overflow Weirs and Other Structures
In cases where there are overflow weirs, gates or other such structures, a numerical simulationis needed that includes models representing the hydraulic characteristics of these structures. The
overflow formula, flow rate coefficient and so on are basically configured with reference to theJapan Society of Civil Engineers Compilation (1999), but, in cases where measured values are able
to be obtained in hydraulic model experiments or other such testing, it is desirable to prepare theconfiguration based on such results.
(4) Implementation of Water Level Fluctuation Simulations Considering Water Intake/Discharge Flow
Rate, Tide Conditions, etc.
The water intake and discharge flow rate affect the initial water level prior to a tsunami strike
as well as hydraulic response characteristics, so boundary conditions need to be configured andthe impact ascertained.
Fluctuation in the water level within the tank attributable to tides may have an effect on
hydraulic response characteristics, so it is necessary to simulate the initial water level in the facility
and the tsunami waveform of the intake and discharge considering tidal conditions. Moreover, incases where the amount of crustal movement occurring due to an earthquake in the surroundingarea may not be disregarded with respect to a sea water intake and discharge, the water level
fluctuation simulation is necessary for which the change in the height of the target facility resulting
from crustal movement is taken into account. In the consideration of crustal movement, it isnecessary to select an appropriate technique in keeping with the assessment method, such as setting
up an arrangement so that the assessment will be on the safe side for the target facility.
(5) Inundation Simulation of Site Considering Overflow from Sea Water Intake and Discharge
Facilities
118

In simulating water level fluctuation of a sea water intake and discharge facilities, in cases
where the water tank water level rises higher than the height of the opening on the water tank top,
the amount of overflow from the water tank is calculated, and an inundation simulation within the
power plant site is performed as necessary. When performing the inundation simulation of the site,a method is generally used that models the site interior using a plane two-dimensional model orother such scheme and gives the calculated overflow amount as a flow rate boundary condition
along the corresponding grids of places where there is overflow from the sea water intake anddischarge facilities. However, in cases where the state of drainage from the site after inundation is
examined, the amount of drainage from inside the site to the sea water intake and discharge
facilities varies depending on the water level within the sea water intake and discharge facilities,
so the examination needs to be performed as a coupled simulation that simultaneously performs
simulations for inside the site and simulations of the water level fluctuation of the sea water intake
and discharge facilities.
6.4 Setting Fault Model Capable of Explaining Run-up Height Record of Past Tsunami
6.4.1 Evaluation of Goodness of Fit of Numerical Model
The goodness of fit of the numerical model is evaluated by using the appropriate topographic
conditions and tsunami source model to conduct an analysis of the tsunami, and then using highly
accurate data of the run-up height of past tsunami to conduct an evaluation based on geometric average

K and geometric standard deviation κ put forth by Aida (1977b).
(1) Evaluation Criteria
Aida (1977b) evaluates the goodness of the fault model based on the geometric average K
and geometric standard deviation κ. The indexes K and κ by Aida (1977b) have been applied asindexes of fitness in space between the run-up height records and calculated heights of tsunami.
The defining equations of K and κ are given as follows.
log K 1 n
 log K i
n i 11  n22 log      log K i   n log K   n  i 1n:number of points for evaluation

Ki  Ri H i
R i : run-up height of past tsunami at i
H i : calculated height of tsunami at i
119

1/2

Since the estimated error of κ depends on the number of points, the number of points should
be stated for reference in calculating K and κ.
(2) Necessity for Reproduction of Topography
The topography of the area around run-up point records of tsunami which are used forverification of reproducibility should be a model that reflects the actual topography when thetsunami occurred to the extent feasible. It is desirable to conduct surveys of transformations of the
topography along the coastline, the state of development of harbors and fishing ports and othersuch features so as to configure the topographic conditions present at the time when the tsunami
occurred.
(3) Method of Selecting Calculation Run-up Height to Contrast with Run-up Point Records of Tsunami
In principle, in cases where the run-up height records of tsunami and the calculation run-up
height of tsunami that ran up onto land are contrasted, the value that is near the grid in which the
run-up point record of tsunami is included is used for the calculation run-up height. However, incases where the tsunami run-up area in the calculation does not extend to the run-up point recordof tsunami and in cases where there are limitations in terms of the topographic representation in
the modeling, a substitution may be made using a calculation run-up height near the run-up point
record of tsunami.
In cases where tsunami inundation simulations are not performed, values are used around thegrid of the coastline which serves as the estimated inrush path to the run-up point records oftsunami. Also, in cases where there is regional deviation in the number of the data distribution for
run-up height records of tsunami and overall reproducibility is regarded as unattainable, it isdesirable to figure out a way to exclude such effects.
(4) Points to be noted
When verifying reproducibility, run-up height records of tsunami which are obtained throughsurveys of past tsunami as presented in Section 3.1 of main volume may be utilized. However,when the reliability of the run-up height records of tsunami is doubtful, the accuracy of the records
must be re-examined based on the original document. If their reliability is determined to be low,
they can be eliminated when evaluating the goodness of fit (see Section 4.8.1 of the appendix
volume).
Since the tide gauge records may provide smaller amplitudes than the run-up height records
of tsunami depending on the period of the tsunamis and the response characteristics of the tidegauges (see Section 4.8.2 of the appendix volume), when the highest tide gauge record is adopted
as a substitute for the run-up height of past tsunami in the evaluation of fit of the fault model, the120systematic differences between the tide gauge records and run-up height records of tsunami must
be carefully considered.
In performing a confirmation of the reproducibility with respect to the results of tsunami
deposits, there is no need to apply the geometric standard deviation κ and geometric mean K put
forth by Aida (1977b). However, the results of tsunami deposits provide information relating to
the height of the minimum level of past tsunami and the extension of the run-up area, so thecalculation results need to exceed these.
6.4.2 Setting Fault Model Capable of Explaining Run-up Height Records of Tsunami of Past Tsunami
The tsunami source parameters of the tsunami source model of the past tsunamis should be
set in such a way to reproduce the distribution of run-up height records of tsunami along the coast.
In General, in cases of tsunami resulting from earthquakes, a source model that can explain
the seismic waves is not always consistent with a model which can explain the run-up heightrecords of tsunami. Needless to say, it aims at the evaluation of the tsunamis considered in thispaper. When the tsunami source model of the past tsunami is set, it is important to also set thetsunami source parameters in order to effectively explain the distribution of the run-up heightrecords of tsunami along the coast well.
(1) General
When the tsunami source model of the past tsunami is set, the tsunami source parameter is
set in such a manner that the run-up height records of tsunami along the coast can be satisfactorily
explained. In other words, the tsunami source parameters should be set so that geometric average

K by Aida (1977b) becomes nearly 1.0, and the geometric standard deviation κ may acquire as low
as possible.
It is recommended to use the following conditions as a good rule of thumb for K and κ ofwide areas (Japan Society of Civil Engineers, 2002).
0.95 < K < 1.05

κ < 1.45
These conditions are essential in order to enable an explanation of the overall trend of the
distribution of the run-up height records of tsunami over a wide area; further, they are also
important for ensuring satisfactory reproducibility in the vicinity of the target site.
When the run-up height records of tsunami for evaluating the reproducibility are selectedtaking the target site into careful consideration, the following criteria should be considered.
1) The distance from the site is short.
2) The number of run-up height records of tsunami necessary for calculating K and κ is121

statistically reliable.
If the tide gauge records can be referred, the parameters should be set so that the wavelength,
phase, etc., of the tsunami can be expressed.
When abundant records are available for recent tsunamis as well as the earthquakes thatcaused them, various characteristics of the earthquake can be referred. These characteristics
include aftershock distribution, focal mechanism solution, crustal deformation before and after theearthquake, etc.
On the other hand, in cases of historical tsunami for which the reliability of run-up heightrecords of tsunami is low, reproducibility on a level equivalent to recent tsunami is not able to be
expected.
(2) Fault Models Proposed in Literature
In the case of major past tsunamis, fault models that can explain tsunami phenomena havebeen proposed in literature, and it is possible to refer to these models when evaluating suchtsunamis. The literature edited by Sato (1989) has a collection of such fault models.
Among these models, the ones from particularly old sources may be inaccurate in the light ofrecent seismological findings in terms of consistency of the depth of plate boundaries, etc. Also,
the grid sizes are roughly drawn leading to a tsunami simulation with poor precision. Therefore,
the parameters of the fault model should be corrected as necessary.
Among the fault models that can explain tsunamis proposed in literatures, there are the models
that can explain not run-up height records of tsunami but tide gauge records. Since the tide gauge
records may provide smaller amplitudes than the run-up height records of tsunami depending on
the period of the tsunamis and the response characteristics of the tide gauges, when the fault modelset by using the tide gauge records is adopted, the systematic differences between the tide gauge
records and run-up height records of tsunami must be carefully considered.
(3) Setting Fault Models Based on Tsunami Inversion Analysis
In cases where a fault model that is appropriate for past tsunami has not been proposed, aneffective method is to set a fault model by means of tsunami inversion analysis. Some typicalmethods are given below.
1) Nonlinear Inversion Analysis
This is a linear approximation iterative solution for a nonlinear model based on the GaussNewton method (see, for example, Nakagawa and Koyanagi, 1991), and, although nonlinear
long-wave theory may be utilized as the numerical model, the simulating time is extensive. The
Central Disaster Management Council (2003) used this method as its application (the ratio of thewater level between coarse-mesh and fine-mesh was used as the conversion coefficient).
1222) Linear Inversion Analysis
A linear inversion analysis where the numerical model is a linear long-wave theory allows
for high-speed and easy simulation but is not able to take into consideration nonlinearity. In
response to the method proposed by Satake (1987), Tanioka and Baba (2004) set forth a method
in which smoothing of the estimation parameters and constraint conditions are given.
3) Linear Inversion Analysis Considering Shallow Water Deformation EffectThis is the tsunami inversion method proposed by Annaka et al. (1999). In the method, themeasured values, excluding the shallow water deformation effect, are regarded as the target
values, and, through repetition of inversion analysis utilizing Green’s function, the method
combines a forward analysis based on nonlinear long-wave theory to converge the results down
into a tsunami source model that considers nonlinear effects.
The parameter, which is estimated by tsunami inversion analysis, is generally magnitude ofslip. Strike direction, dip angle, slip angle and other elements are configured in advance based onseismological knowledge and the region enveloping the anticipated tsunami source region isdivided into multiple small faults so that the slip distribution of the individual small faults is able
to be found using inversion analysis. In cases where there are a high number of small faults, theunknown quantity (number of groups estimating slip) may be reduced by dividing the region into
groups where the slip is assumed to be the same.
Records of tsunami tidal observations, run-up height records of tsunami, records of crustal
movements and other such elements are used as the objects of reproduction in the tsunami
inversion analysis and the fault slip, for which the residual sum of squares of these observed
values and the calculated values are the smallest, is found as the optimal solution. However, withhistorical tsunami for which tidal observation records or other measurement records are
insufficiently available, the solution becomes unstable when the number of the unknown number
increases, so creative schemes are necessary such as limiting the unknown number or assuming
constraints and smoothing as proposed by Tanioka and Baba (2004).
For tsunami inversion analysis of the 2011 Tohoku Earthquake, sufficient observation
records are available, and Satake et al. (2013), Sugino et al. (2013), Takao et al. (2012) and others
have reported case studies in which inversion analyses where fault rupture propagation and timelag are taken into consideration have been performed.

1236.5 Assessment of Tsunami Wave Force
6.5.1 Basic Approach
In cases where a tsunami reaches seawalls, buildings or other such structures, the tsunami wave
force (hereinafter, “tsunami wave pressure” is included in the term “tsunami wave force”) needs to beappropriately calculated so as to ascertain the impact to the facility. With respect to the tsunami wave
force, after taking into account the location where the structures to be assessed are located (maritime
or land), the appropriate assessment formula is utilized to calculate the tsunami wave force based ontsunami water level, inundation depth, temporal change in flow velocity and other such data.
Although sufficient knowledge has not become available about tsunami wave forces acting on
the ground in the vicinity of structures, research case studies on this issue are given in Section 8.1.3
of appendix volume. Also, in cases where application of previous assessment formula is considereddifficult or other such similar situations, hydraulic model experiments and three-dimensional
numerical simulation can be performed.
6.5.2 Calculation of Tsunami Wave Force
The hydraulic quantity (water level, inundation depth, flow velocity) obtained from the tsunami
propagation and run-up simulations is used to calculate, using the appropriate assessment formula, thetsunami wave force acting on a structure in accordance with the type of tsunami wave pressure,conditions of the tsunami impact (presence of soliton fission, etc.), profile of the targeted structure,etc. The points noted below should be kept in mind for appropriately selecting the formula forassessment of tsunami wave force.
(1) Hydraulic Quantity Used for Calculation of Tsunami Wave Force
For calculation of tsunami wave force, there are hydraulic quantity in which water level (inthe case of maritime structures) or inundation depth (in the case of land structures) obtained fromtsunami propagation and run-up simulations are used, and hydraulic quantity where flow velocity
is used, in addition to these. For this reason, it is necessary to calculate the appropriate hydraulicquantity in accordance with the assessment formula utilized.
(2) Type of Tsunami Wave Pressure
Arikawa et al. (2005) classified the tsunami wave pressure acting on an upstanding wall using
a time series as shown in Figure 6.5.2-1. In other words, the tsunami wave pressure is classified
by the wave pressure that develops during the action of the tsunami head (hydro dynamic pressure)124and the wave pressure that develops due to the continuous arrival of incident ways (continuouspressure). Among the assessment equations that have been proposed, there are the equations thatcan estimate hydro dynamic pressure and continuous pressure in a time series, those that focus
only on maximum continuous pressure, and those that estimate the maximum tsunami wave
pressure regardless of the type of tsunami wave pressure. For this reason, after closely scrutinizing
the process through which each assessment formula is derived, the appropriate assessment formulaneeds to be selected in keeping with the type of tsunami wave pressure to be estimated.
With respect to inclined-type maritime structures, the classification of tsunami wave pressure
is more complicated as, in addition to the classifications shown in Figure 6.5.2-1, there is tsunami
wave pressure that develops when there is run-up over a slope, tsunami wave pressure thatdevelops when incident waves and reflective waves collide on a slope, and other types of tsunami
wave pressures. Mizutani and Imamura (2000) and Mizutani and Imamura (2002) classified
tsunami wave pressures acting on inclined-type structures and proposed assessment formulas foreach (see Section 8.1.1 in the appendix volume).

Hydro dynamic pressure
Wave波圧pressure

Develops during
津波先端部
actionof tsunami
作用時に発生head

Continuous pressure
Develops with continuous arrival of
入射波の連続的な到達により発生
incident tsunami

Impulsive hydro dynamic
衝撃津波波圧pressure
Maximum continuous pressure
最大重複波圧時間
Time

Figure 6.5.2-1 Classification of tsunami wave pressure (Arikawa et al., 2005)(3) Presence of Soliton Fission
In cases where undular bore develops, which has a bore shape at the head of a tsunami witha long wavelength and splits into multiple short wavelength waves (soliton fission), the impulsive
force is increased. Accordingly, an assessment is performed for whether or not soliton fission
develops, and an assessment formula where this is taken into account needs to be used in cases
where the development of soliton fission is anticipated.

125

(4) Profile of Target Structures
The profile of structures can be classified into three-dimensional structures such as buildings
where a tsunami flows into the back through both sides of the structure, and two-dimensional
structures (linear structures) such as seawalls that are homogenous in a cross direction and there isno inflow of the tsunami into the back except for overflow. In the calculation of tsunami wave
force, assessment formula needs to be utilized that is appropriate in keeping with the profile of thetarget structure (three-dimensional structure, two-dimensional structure).
6.5.3 Features of Tsunami Wave Force Assessment Formulas
Separated into those for a tsunami wave force acting on maritime structures and tsunami wave
force acting on land structures, previous assessment formulas and their features are presented. The
specific details of the respective assessment formulas are given in Sections 8.1.1 and 8.1.2 of theappendix volume. In addition, case studies verifying the validity of tsunami wave force assessment
formulas are presented in Section 8.1.4 of the appendix volume.
6.5.3.1 Tsunami Wave Force Acting on Maritime Structures(1) Classification of Assessment Formulas for Tsunami Wave Force Acting on Upright Maritime
Structures
In the Ministry of Land, Infrastructure, Transport and Tourism (2013), the experience of the2011 Tohoku Earthquake was taken into account and a classification was worked out as shown in
Table 6.5.3-1 for tsunami wave forces used in verification of the stability of the upright portion ofcomposite-type breakwaters, and respective assessment formulas have been proposed.

126

Table 6.5.3-1 Classification of formulas for assessing tsunami wave force acting on upright maritime
structures
Tsunami wave force
assessment formula

Presence oftargetstructuressubject totsunamisimulation

Ikeno et al. (2005)

With
structures

Tanimoto et al.
(1984)

With
structures

Ministry of Land,
Infrastructure,
Transport andTourism (2013)

With
structures

Hydraulicquantity used intsunami wave
force calculation
Maximumtsunami waterlevel
Maximumtsunami waterlevel
Maximum waterlevel differenceType of tsunami
wave pressure

Presence ofsoliton fission

Profile of target
structure

Presence ofoverflow

Impulsive hydrodynamic pressure

FissionTwo-dimensional
structure

Overflow andnon-overflow

Impulsive hydrodynamic pressure

Non-fission

Two-dimensional
structure

Non-overflow

Maximum
continuouspressureNon-fission

Two-dimensional
structure

Overflow(2) Classification of Assessment Formulas for Tsunami Wave Force Acting on Inclined Maritime
Structures
With respect to formulas for assessing tsunami wave force acting on inclined maritime
structures, a classification of the assessment formulas that have been proposed is shown in Table
6.5.3-2.
Table 6.5.3-2 Classification of formulas for assessing tsunami wave force acting on inclined maritime
structures
Tsunami wave
force assessment
formulaPresence oftargetstructuressubject totsunamisimulation

Hydraulicquantity used intsunami wave
force calculation

Type of tsunami
wave pressure*Presence ofsoliton fission

Profile of target
structure

Presence ofoverflow

Fukui et al.
(1962)
Mizutani and
Imamura (2000)
Mizutani and
Imamura (2002)

No structure

Incident wave
height and wave
velocity

Hydro dynamic
pressure andimpulsive hydrodynamic pressure

Non-fission

Two-dimensional
structure

Non-overflow

Mizutani and
Imamura (2000)

No structure

Incident wave
height and wave
velocity

Run-up pressure

Non-fission

Two-dimensional
structure

Non-overflow

Mizutani and
Imamura (2000)

No structure

Incident wave
height and wave
velocity

Non-fission

Two-dimensional
structure

Non-overflow

Mizutani and
Imamura (2002)

With
structure

Crown maximum
flow velocity

Non-fission

Two-dimensional
structure

Overflow

Impact continuouspressure andimpulsive impact
continuous pressure
Overflow pressure
and impulsive
overflow pressure* Classification based on Mizutani and Imamura (2000) and Mizutani and Imamura (2002) (See
Section 8.1.1 in the appendix volume)127

6.5.3.2 Tsunami Wave Force Acting on Land Structures(1) Classification of Assessment Formulas for Tsunami Wave Force Acting on Land Structures
Classification of formulas which have been proposed for assessing tsunami wave force acting
on land structures is shown in Table 6.5.3-3. The tsunami wave force assessment formulas areclassified depending on whether or not the target structures in the tsunami inundation simulation
are taken into consideration, hydraulic quantity used in tsunami wave force calculation, type oftsunami wave pressure, presence of soliton fission, and the profile of target structures.
Table 6.5.3-3 Classification of formula for assessing tsunami wave force acting on land structures
Tsunami wave
force assessment
formulaPresence oftargetstructuressubject totsunamisimulation

Hydraulic quantity usedin tsunami wave force
calculation

Type of tsunami wave pressure

Presence ofsoliton fission

Profile of target
structure

Asakura et al.
(2000)

Maximum inundation
depth

Impulsive hydro dynamic
pressure and maximum
continuous pressure

Fission andnon-fission

Two-dimensional
structure

Ikeno et al.
(2006)

Maximum inundation
depth

Impulsive hydro dynamic
pressure and maximum
continuous pressure

Fission andnon-fission

Two-dimensional
structureThree-dimensional
structure

Cabinet Office(2005)

Maximum inundation
depth

Impulsive hydro dynamic
pressure and maximum
continuous pressure

Non-fission

Three-dimensional
structure

Ministry of Land,
Infrastructure,
Transport andTourism (2012)

Maximum inundation
depth

Impulsive hydro dynamic
pressure and maximum
continuous pressure

Non-fission

Three-dimensional
structure

No structure
Fire and Disaster
Management
Agency (2009)

Maximum inundation
depth
Maximum inundation
depth and flow velocity

Impulsive hydro dynamic
pressure and maximum
continuous pressure
Impulsive hydro dynamic
pressure and maximum
continuous pressure
Impulsive hydro dynamic
pressure and maximum
continuous pressure

Non-fission

Non-fission

Asakura et al.
(2002)

Maximum inundation
depth and flow velocity

Sakakiyama(2012)

Maximum inundation
depth and flow velocity

Omori et al.
(2000)

Inundation depth andflow velocity

Iizuka andMatsutomi (2000)

Maximum inundation
depth

Maximum continuous pressure

Non-fission

Arimitsu et al.
(2012)

Inundation depth andflow velocity

Hydro dynamic pressure andcontinuous pressure (timeseries)Non-fission

Inundation depth andflow velocity
Inundation depth andflow velocity

Continuous pressure (timeseries)Continuous pressure (timeseries)Kihara et al.
(2012)
Takabatake et al.
(2013)

With structure

Impulsive hydro dynamic
pressure and maximum
continuous pressure
Hydro dynamic pressure andcontinuous pressure (timeseries)128

Non-fission

Two-dimensional
structure(Dike)
Three-dimensional
structure(Cylindrical tank)Two-dimensional
structureThree-dimensional
structure

Non-fission

Two-dimensional
structure

Non-fission

Three-dimensional
structure

Non-fission
Non-fission

Three-dimensional
structure
Two-dimensional
structureThree-dimensional
structureThree-dimensional
structure
Two-dimensional
structure(2) Presence of Target Structures in Tsunami Inundation Simulation and Method of Applying
Assessment Formula
The formulas that have been proposed for assessment of tsunami wave force are categorized
into equations assessing tsunami wave force based on the specifications of incident tsunami underconditions where there is no structural impact, and equations assessing tsunami wave force basedon the specifications of tsunami under conditions where structural impact is taken into
consideration.
In the tsunami inundation simulation, major structures within the target site are considered as
topographic data, so, in cases where the results of tsunami inundation simulations without any
structures are used to calculate the tsunami wave force, the tsunami inundation simulation is
performed under conditions where the target structures or all structures have been removed. In theassessment formulas, where the results of tsunami inundation simulations with structures are used,
the hydraulic quantity that has sustained structural impact is used to calculate tsunami wave force,so the results of tsunami inundation simulations where structures have been taken into
consideration.
Cases focusing on structures in water channels are the examples where application of theformer assessment formula is not easy. At this time, the greater the width of a structure becomesin proportion to the water channel width, the higher the blockage ratio of the water channel
becomes and the greater the water depth in front of the structure. As a result, even if thespecifications of inflowing tsunami and pass-through tsunami are constant, the tsunami wave
pressure acting in front of the structure will become greater. In other words, tsunami wave pressure
does not depend only on the specifications of inflowing tsunami and pass-through tsunami, andapplication of the former assessment formula may be difficult.
An example where application of the latter assessment formula is not simple may be seen ina case where the grid size for numerical simulations is larger than the size of the target structure.
At this time, the impact that the structure has on flow is not able to be appropriately expressed innumerical simulations. Accordingly, in such a case, the accuracy of the data input into the latterassessment formula becomes lower and the precision of the tsunami wave pressure estimated as aresult decreases. For this reason, the latter assessment formula is suited to the calculation oftsunami wave force acting on structures that is able to be represented using a certain number ofgrids. For example, numerical simulation solving for tsunami flow within a power plant site usinga grid resolution of several meters is suited to the computation of tsunami wave force with respect
to seawalls, buildings of tens of meters in width and other such structures.

129

6.6 Sediment Transport Simulation
6.6.1 Basic Approach
The impact that the transport of sediment due to a tsunami may have on a nuclear power facility
includes, for example, a decline in water intake function resulting from deposits of sand in front of thewater intake opening as well as structures collapsing and being swept away by scouring from sandaround a breakwater or other such structure. In cases where the impact of such phenomena is assessed,
it is necessary to use the appropriate topography change prediction model to simulate sedimenttransport so as to assess deposits of sand in front of water intake openings, scouring around structuresand other such effects.
Erosion, sedimentation and scouring due to the transport of sediment on the seafloor when atsunami occurs affects the safety of port and coastal facilities such as revetments, so a topographychange prediction model allowing for a high level of reproducibility is required, and research has been
conducted on the development of such models as well as verification of their validity.
Takahashi et al. (1992), Takahashi et al. (1999) and Fujii et al. (1998) have conducted researchon the prediction of topography change due to tsunami and developed prediction models. Also, Ikeno
et al. (2009) has proposed a new pickup rate equation of suspended sediment where the effect of sandgrain size dependence is taken into consideration based on data about flow velocity and suspended
sediment concentration obtained from the experiments of sediment transport model. Takahashi et al.
(2011) used hydraulic model experiments to find a pickup rate equation and bed load equation where
sand grain size dependency is taken into account. Morishita and Takahashi (2014) focused on thefactors that have a dominant effect on sediment transport and suggested the possibility of improvement
the model.
From the standpoint of model verification, Fujii et al. (1998) and Takahashi et al. (1999)
conducted the assessments of field applicability by numerical simulating topography change in
Kesennuma bay when the 1960 Chile tsunami struck. Also, Fujii et al. (2009) carried out theverification by numerical simulating of topography change, which was obtained from the experiments
conducted by Ikeno et al. (2009).

130Initial conditions
・Fault model・Topography
・Structures
・Friction coefficient

Forward time step

Tsunami propagation simulation
・Continuity equation
・Momentum equation

Calculation of bottom shear stress

Topography change simulation
・Bed load equation
・ Calculation of suspended
sediment concentration

Amount of topography change
Correction of topography

Figure 6.6.2-1 Flowchart of sediment transport simulation attributable to tsunami

6.6.2 Selection of Numerical ModelIn the selection of a numerical model for sediment transport simulation, an appropriate numericalmodel is selected that is able to calculate with even better precision erosion, sedimentation andscouring from sand attributable to tsunami.
Flowchart showing the course of the sediment transport simulation caused by tsunami is shownin Figure 6.6.2-1. The sediment transport simulation is performed by separating into a fluid layer andsand layer. First, a tsunami propagation simulation is performed to calculate shear stress in the fluidlayer. Next, topography change is simulated in the sand layer. The topography change simulation of
the sand layer solves the continuity equation

for sediment and the bed load equation, and the bed

load equation estimates the bed load sediment rate by using the bottom shear stress transferred fromthe fluid layer. With the continuity equation for sediment, topography change due to the estimatedsediment transport rate is found to update the topography.
Although the process commonly employed in the sediment transport simulation is as describedabove, the following three points differ significantly depending on the model applied.
・

Assessment of bottom shear stress・

Bed load equation

・

Pickup rate equation and deposition rate equation

The methods proposed by Fujii et al. (1998), Ikeno et al. (2009), Takahashi et al. (1999) and131

Takahashi et al. (2011) are the major models where bed load and suspended sediment are taken into
consideration. With respect to these methods, the continuity equation for bed load sediment, continuity
equation for suspended sediment concentration, bed load equation, pickup rate equation, deposition
rate equation and friction velocity equation are shown in Table 6.6.2-1 (see Section 8.2.1 of theappendix volume for detailed commentary). Examples of sediment transport simulations are given in
Sections 8.2.2 and 8.2.3 of the appendix volume.
Table 6.6.2-1 Summary of sediment transport simulation methods
Fujii et al. (1998) method

Takahashi et al. (1999) andIkeno et al. (2009) method(2011) methods
Continuity equation
for bed load
sediment
Continuity equation
for suspended
sediment
concentration

ESZ Q 
0
 

t
 x   (1   )Z
1  Q E  S 



0
t 1    x Z1  Q E－ S   0

t 1    xC UC  E  S
 
0
－
t
D
 x 

 (C s D )  ( MC s ) E  S

0


x
t

C D  CM
ES 0txExperimental formula by
Kobayashi et al. (1996)

Experimental formula by
Takahashi et al. (1999)

Experimental formula by
Ashida et al. (1972)

Q  80 1.5 sgd 3

Q  21 1.5 sgd 3

Q

Experimental formula by
Takahashi et al. (2011)

sgd 3

Bed load equation 17 3 / 2 (1   c /  ) 1  ( c /  )1 / 2

Q  5.6 1.5 sgd 3 (d  0.166mm)
Q  4.01.5 sgd 3 ( d  0.267 mm )Q  2.6 1.5 sgd 3 (d  0.394mm)

E

Pickup rate equation(1   )Qw2 (1   )  wD 
Uk z 1  exp k z 
Experimental formula by
Takahashi et al. (1999)
E  0.012 2 sgd  Experimental formula by
Takahashi et al. (2011)E  7.0  10 5  2 sgd   ( d  0.166 mm )E
 a ( 2 / sgd 3 ) 0.2 ( w /sgdsgd ) 0.8 (   c )*Coefficient a is a range of 0.1~ 0.2 determined based on
previous experimental
results

E  4.4  10 5 2 sgd   ( d  0.267 mm )E  1.6  10 5 2 sgd   ( d  0.394 mm )Deposition rateequationS  wC b

S  wCs  Friction velocity
equation

Calculated using the formulacalculated by intergrating thelog-wake law verticallyCalculated using Manning’s law

S  wC bu*  gn U / D
2

132

2

1/ 3

Calculated using the formulacalculated by intergrating thelog-wake law vertically2

Guide to symbols

Z : Amount of change in water depth [m]Q : Bed load sediment rate per unit width and unit time [m3/s/m]
 : Shields numberc : Critical shields numbers : Underwater specific gravity of sediment (σ/ρ-1)
g : Gravitational acceleration [m/s2]
U : Flow velocity [m/s]M : Flow rate per unit width U×D[m2/s]
n : Manning’s coefficient of roughness [m-1/3･s]
α : Ratio that component whose movement is dominated only by localized external force accounts forof all sediment transport rate (=0.1; based on Fujii et al., 1998)
w : Settling velocity of sand grains (Rubey, 1993) [m/s]Z0 : Roughness height (=ks/30) [m]kz : Vertical diffusion coefficient (=0.2κu*h; based on Fujii et al., 1998) [m2/s]
ks : Equivalent roughness [m]κ : Karman constant (=0.4; based on Fujii et al., 1998)h : Water depth [m]C , Cb: Suspended sediment concentration, bottom suspended sediment concentration [kg/m3]
C : Mean suspended sediment concentration
Cs : Suspended sediment volume concentration
log-wake law: Equation adding wake function (Fujii et al., 1998) to logarithmic law
u* /U   /[ln(h / Z0 ) 1]
t : Time [s]x : Plane coordinates
σ : Density of sand [kg/m3]
d : Sand grain size [m]ρ : Density of seawater [kg/m3]
D : Total water depth [m]λ : Porosity
ν : Kinematic viscosity coefficient [m2/s]

133

6.6.3 Simulating Conditions and Coefficients
When simulating sediment transport, the simulating conditions and other parameters are set bycollecting and analyzing information such as boring survey results and geologic distribution charts
about the vicinity of the assessment points as presented in Section 3.4 of main volume.
(1) Initial Sand Distribution and Sediment Thickness
Based on the results of surveys of bottom sediment in the surrounding sea areas and othersuch data, the planar sand layer distribution is confirmed. In cases where information is available
about sediment thickness, the erosion and scouring maximum limit of thickness is configured. Also,in cases where information is not available about sediment thickness, the erosion and scouring
maximum limit of thickness may also be configured as an infinite thickness.
(2) Grain Size and Density
Based on the results of surveys of bottom sediment in the surrounding sea areas and othersuch data, the median grain size and density of sand is configured.
(3) Upper Concentration Limit for Suspended Sediment
The characteristics of method are taken into account to appropriately configure the upper
concentration limit for suspended sediment based on the results of previous research. Examples ofprevious research on the upper concentration limit for suspended sediment are given in Section
8.2.3.3 of the appendix volume.
Configurations of the upper concentration limit for suspended sediment have been verified in
actual sea areas, and these research results may be referenced. Fujita et al. (2010) used the methods
proposed by Takahashi et al. (1999) and Ikeno et al. (2009) to verify the extent of topographychange in Hachinohe port that resulted from the 1960 Chile tsunami, and obtained results showing
good reproducibility in the case that an upper concentration limit for suspended sediment is 1 to
2%. Also, Imai et al. (2015) formulated the saturated suspended sediment concentration as afunction of flow velocity in order to take into account that the saturated suspended sedimentconcentration changed following water turbulence.
(4) Porosity
The porosity of sediment is configured based on a general value. Takahashi et al. (1992) used
0.4 for it.

134

(5) Settling Velocity
The settling velocity of sand grains is calculated based on Rubey (1933) and other sources.
(6) Grid Size
An appropriate grid size is configured so that the tsunami flow velocity, which is important
for the sediment transport simulation, is able to be reproduced.
6.7 Assessment of Debris
6.7.1 Behavior of Debris
6.7.1.1 Basic ApproachWith regard to debris that is generated by tsunami, the behavior of debris needs to be understoodin cases where it is conceivable there is the possibility of debris colliding with structures, equipment
or other such items or the debris blocking water intake channels and other such pathways.
The behavior of debris during tsunami is based on the appropriate configuration which is inaccordance with the temporal change of inundation depth, flow velocity, flow direction and other suchcharacteristics, which are determined from a plane two-dimensional model that is based on the
nonlinear long-wave theory. In recent years, research has been advanced on methods to analyze thebehavior of tsunami and the behavior of debris (floating, collision, submersion, etc.) at the same time,
and these methods may also be utilized after verifying the applicability of them.
6.7.1.2 Examples of Past Research Studies on Debris Numerical Methods
With regard to wood and lumber, Goto (1983) proposed a movement simulation where the inertia,
the pressure gradient of water flow, additional mass, drift wood resistance and diffusion are taken into
consideration in the movement of wood and lumber in a horizontal direction.
With respect to ships and vessels, Fujii et al. (2005) used the Distinct Element Method (DEM) to
calculate the debris behavior of vessels and compared these with the results of hydraulic modelexperiments. This method is not only applicable to ships and vessels but also to other types of debris.
In addition, Kobayashi et al. (2005), Honda et al. (2009) and Hashimoto et al. (2010) have proposed
methods for calculating the behavior of ships and vessels using a momentum equation where surging,swaying and yawing are taken into consideration. Also, in recent years, the methods have been
proposed that include a method in which a solid-gas-liquid multi-phase model for conducting flow
simulation including solid phase is used (Kawasaki et al., 2007), a method to solve a momentum
135equation where three translational degrees of freedom and three rotational degrees of freedom aretaken into consideration (Yoneyama and Nagashima, 2009), a method in which the particle method isapplied to calculate behavior of debris (Goto et al., 2009), and a method coupling the Distinct Element
Method (DEM) to the gas-liquid two-phase model to calculate behavior of debris (Ikeda and Arikawa,2014).
Examples of calculations of debris numerical methods are given in Section 8.3.3 of the appendix
volume.
6.7.2 Calculation of Impact Force Attributable to Debris
6.7.2.1 Selection of Debris and Collide Objects
In calculating the impact force due to debris, objects which becomes debris are selected on thebasis of the results of surveys of debris as presented in Section 3.5 of main volume as well as tsunami
water level, flow velocity and other hydraulic quantity. The assessment method proposed by Ikeno andTanaka (2003) is referenced with respect to the selection of objects which becomes debris. Also, incases where the specifications of objects collided with are necessary for the calculation of impact force,
objects collided with, which are object to assessment, are determined along with the selection of
objects which becomes debris.
6.7.2.2 Calculation Method for Impact ForceIn the assessment of the impact force of debris, calculations are performed by using theappropriate impact force calculation equation based on specifications of debris and drifting speed. The
drifting speed is appropriately configured based on the hydraulic quantity (tsunami water level,
inundation depth, flow velocity, flow direction, etc.) obtained from the results of numerical simulations
based on nonlinear long-wave theory.
Specific details about impact force calculation equations for major debris, which have been
proposed, are given in Section 8.3.1 of the appendix volume. With respect to impacts of debris,
calculation equations to assess such impacts using “force” and calculation equations to assess suchimpacts using “energy” have been proposed, but, in this publication, calculation equations to assess
impact of debris by means of “force” are compiled in Section 8.3.1 of the appendix volume.
6.7.2.3 Selection of Impact Force Calculation Equations
With regard to the impact force of debris, a variety of calculation equations have been proposed136

for drift wood and containers. However, there are currently many points that have not been sufficiently
clarified, and cases of verification and practical application are limited, and quantitative assessment
methods have not been established. Accordingly, in the calculation of impact force attributable todebris, it is desirable to utilize a calculation equation after closely examining the underlying
assumptions of various calculation equations with respect to debris, drifting, impact and other suchelements. Examples of impact force calculation equations whose validity has been verified are given
in Section 8.3.2 of the appendix volume.

[Chapter 6 References]
Aida, I. (1969): Numerical Experiments for the Tsunami Propagation - the 1964 Niigata Tsunami andthe 1968 Tokachi-oki Tsunami, Bulletin of the Earthquake Research Institute, University ofTokyo, Vol.47, pp. 673-700.
Aida, I. (1975): Numerical Experiments of the Tsunami Associated with the Collapse of Mt.
Mayuyama in 1792, Zisin: Journal of the Seismological Society of Japan, Second Series, Vol.
28, pp. 449-460 (in Japanese).
Aida, I. (1977a): Numerical Experiments for Inundation of Tsunamis: Susaki and Usa, in Kochi
Prefecture, Bulletin of the Earthquake Research Institute, The University of Tokyo, Vol.52, pp.
441-460 (in Japanese).
Aida, I. (1977b): Simulations of Large Tsunamis Occurring in the Past off the Coast of the Sanriku
District, Bulletin of the Earthquake Research Institute, The University of Tokyo, Vol. 52, pp.
71-101 (in Japanese).
Annaka, T., K. Ota, H. Motegi, I. Yoshida, M. Takao and H. Soraoka (1999): Tsunami Inversion Basedon the Shallow Water Theory, Proceedings of Coastal Engineering, JSCE, Vol. 46, pp. 341-245(in Japanese).
Arikawa, T., M. Ikebe, F. Yamada, K. Shimosako and F. Imamura (2005): Large-Scale Experiments ofTsunami Wave Force on Revetments and Land Structures, Annual Journal of Coastal
Engineering, JSCE, Vol. 52, pp. 746-750 (in Japanese).
Arikawa, T., F. Yamada and M. Akiyama (2005): Study of Applicability of Tsunami Wave Force inThree-Dimensional Numerical Wave Tank, Annual Journal of Coastal Engineering, JSCE, Vol.
52, pp. 46-50 (in Japanese).
Arikawa, T. and M. Washizaki (2010): Large scale tests on concrete wall destruction by tsunami withdriftwood, Journal of the Japan Society of Civil Engineers, Ser. B2 (Coastal Engineering), Vol.
66, No. 1, pp. 781-785 (in Japanese).
Arimitsu, T., K. Ooe and K. Kawasaki (2012): Proposal of Evaluation Method of Tsunami Wave
137

Pressure Using 2D Depth-Integrated Flow Simulation, Journal of the Japan Society of Civil
Engineers, Ser. B2 (Coastal Engineering), Vol.68, No.2, pp. I_781-I_785 (in Japanese).
Asakura, R., K. Iwase, T. Ikeya, M. Takao, T. Kaneto, N. Fujii and M. Ohmori (2000): Empirical Studyof Wave Force Caused by Tsunami Overflowing Revetments, Proceedings of Coastal
Engineering, JSCE, Vol. 47, pp. 911-915 (in Japanese).
Asakura, R., K. Iwase, T. Ikeya, M. Takao, N. Fujii and M. Ohmori (2002): THE TSUNAMI WAVEFORCE ACTING ON LAND STRUCTURES, Proceedings of 28th International Conference
on Coastal Engineering, Vol. 28, pp. 1191-1202.
Ashida, K. and M. Michiue (1972): Study on Hydraulic Resistance and Bed-load Transport Rate inAlluvial Streams, Japan Society of Civil Engineers Collection of Papers and Reports, No. 206,
pp. 59-69 (in Japanese).
Cabinet Office (2005): Guidelines on Tsunami Evacuation Buildings, etc.
(in Japanese).
Cabinet Office (2012): Mega Earthquake Model conference for the Nankai Trough (Second Report)
Tsunami Fault Model Compilation: Tsunami Fault Models and Tsunami Height andInundation Areas, etc. (in Japanese).
http://www.bousai.go.jp/jishin/nankai/model/pdf/20120829_2nd_report01.pdf (Accessed on
August 2016)
Cerjan, C., D. Kosloff, R. Kosloff and M. Reshef (1985): A nonreflecting boundary condition for
discrete acoustic and elastic wave equations, Geophysics, Vol. 50, No. 4, pp. 705-708.
Central Disaster Management Council (2003): Calculation Method of Tsunami Source Area Using
Inversion, Committee for Technical Investigation on Countermeasures for the Tonankai andNankai Earthquakes (16th), Reference Material 2-7 (in Japanese).
Coastal Development Institute of Technology (2010): Research and Development on CADMASSURF/3D, Report of Study Group on Application of Three-Dimensional Numerical Wave Tank
to Maritime Structures Design, Coastal Technology Library, No. 39 (in Japanese).
Electric Power Civil Engineering Association, Editor (1995): Design of Civil Engineering Structures
for Thermal and Nuclear Power Plants; Supplemental Revised Edition, pp. 786-833 (inJapanese).
Express Highway Research Foundation of Japan (1985): Research Report on Stability Assessment ofLandslide Terrain, Japan Highway Public Corporation (in Japanese).
Fire and Disaster Management Agency (2009): Investigative Report on Tsunami and Inundation
Countermeasures for Hazardous Material Facilities (in Japanese).
Fujii, N., M. Omori, M. Takao, S. Kanayama, H. Otani (1998): Study on Numerical Model of
Topography Change due to Tsunami, Proceedings of Coastal Engineering, JSCE, Vol. 45, pp.
376-380 (in Japanese).
138

Fujii, N.., M. Omori, T. Ikeya, R. Asakura, T. Takeda, and K. Yanagisawa (2005): Numerical Analysis
of Tsunami Debris in Ports, Annual Journal of Coastal Engineering, JSCE, Vol. 52, pp. 296300 (in Japanese).
Fujii, N., M. Ikeno, T. Sakakiyama, M. Matsuyama, M. Takao and T. Mukohara (2009): HydraulicExperiment on Flow and Topography Change in Harbor due to Tsunami and Its Numerical
Simulation, Journal of the Japan Society of Civil Engineers, Vol. 56, pp. 291-295 (in Japanese).
Fujita, N., K. Inagaki, N. Fujii, M. Takao and T. Kaneto (2010): Study on Field Applicability of
Estimation Model for Topography Change due to Tsunamis, Annual Journal of Civil
Engineering in the Ocean, JSCE, Vol. 26, pp. 213-218 (in Japanese).
Fukui, Y., H. Shiraishi, M. Nakamura and Y. Sasaki (1962): Tsunami Research (II) Bore-Type Tsunami
Impact on Coastal Dike, 9th Coastal Engineering Committee Proceedings, pp. 50-54 (inJapanese).
Goto, C. and Y. Ogawa (1982): Numerical Calculation Method Using the Leapfrog Method, Tohoku
University of Engineering Department of Civil and Environmental Engineering Material, 52p.
(in Japanese).
Goto, C. (1983): Calculation of Outflow of Timber due to Tsunami, Proceedings of the 30th Japanese
Conference on Coastal Engineering, pp. 594-597 (in Japanese).
Goto, C. and N. Shuto (1983): Numerical Simulation of Tsunami Propagation and Run-up, Tsunamis:
Their Science and Engineering, pp. 439-451.
Goto, C. and K. Sato (1993): Development of Tsunami Numerical Simulation System for Sanriku
Coast in Japan, Port and Harbour Research Institute, Vol. 32, No. 2, pp. 3-44 (in Japanese).
Goto, H., H. Ikari, K. Tonomo, T. Shibata, Tomoya Harada and Atsunori Mizoe (2009): Numerical
Analysis on Drifting Behavior of Container on Apron due to Tsunami by Particle Method,
Journal of the Japan Society of Civil Engineers, Ser. B2 (Coastal Engineering), Vol.B2-65,
No.1, pp. 261-265 (in Japanese).
Goto, H., H. Ikari, T. Matsubara and T. Ito (2011): Numerical Simulation on Tsunami due to Sector
Collapse by Solid-Liquid Two-Phase Flow Model Based on Accurate Particle Method, Journalof the Japan Society of Civil Engineers, Ser. B2 (Coastal Engineering), Vol. 67, No. 2, pp.
I_196-I_200 (in Japanese).
Hara, N., H. Iwase and C. Goto (1998): Multi-step Mixed Finite Difference Scheme for Nonlinear
Dispersive Long Wave Theory, Proceedings of Coastal Engineering, JSCE, Vol. 45, pp. 26-30(in Japanese).
Hasegawa, K., T. Suzuki, K. Inagaki and N. Shuto (1987): A Study on the Mesh Size and Time
Increment in the Numerical Simulation of Tsunamis, Proceedings of Japan Society of Civil
Engineers, No. 381/II-7, pp. 111-120 (in Japanese).
Hashi, K. and F. Imamura (2000): Study on Multi-Tsunami Source in the Case for the 1998 Papua
139

New Guinea Tsunami, Proceedings of Coastal Engineering, JSCE, Vol. 47, pp. 346-350 (inJapanese).
Hashimoto, T., S. Koshimura, E. Kobayashi, N. Fujii and M. Takao (2010): Development of Hazard
Map in Waterfront Area by Ship Drifting and Grounding Model in Tsunami, Journal of theJapan Society of Civil Engineers, Ser. B2 (Coastal Engineering), Vol. 66, No. 1, pp. 236-240(in Japanese).
Hino, M. and E. Nakaza (1988): Application of New Non-Reflective Boundary Scheme to Plane TwoDimensional Problems in Numerical Wave Motion Analysis, Proceedings of the 35th Japanese
Conference on Coastal Engineering, pp. 262-266 (in Japanese).
Hiraishi, T., H. S. and N. Hara (2001): Reproduction of Meiwa Yaeyama Earthquake-Tsunami with
Landslide Tsunami Source Using Circular Slip Method, Proceedings of Coastal Engineering,
JSCE, Vol. 48, pp. 351-355 (in Japanese).
Honda, K., T. Tomita, D. Nishimura and A. Sakaguchi (2009): Numerical Modeling of Tsunami
Drifted Bodies, Annual Journal of Civil Engineering in the Ocean, JSCE, Vol. 25, pp. 39-44(in Japanese).
Honma, M. (1940): Flow Rate Coefficient for Low-Overflow Dams, Journal of the Japan Society of
Civil Engineers, Vol. 26, No. 6, pp. 635-645, No. 9, pp. 849-862 (in Japanese).
Iizuka, H. and H. Matsutomi (2000): Estimation of Damage from Tsunami Inundated Flow,
Proceedings of Coastal Engineering, JSCE, Vol. 47, pp. 381-385 (in Japanese).
Ikeda, T. and T. Arikawa (2014): Study on the Drifting Container Motion by using Solid-Gas-Liquid
Coupled CADMAS-SURF/3D, Journal of the Japan Society of Civil Engineers, Ser. B2(Coastal Engineering), Vol. 70, No. 2, pp. I_331-I_335 (in Japanese).
Ikeno, M. and H. Tanaka (2003): Experimental study on impulsive force due to collision of driftedbody and Tsunami Run-up on Land, Proceedins of Coastal Engineering, JSCE, Vol. 50, pp.
721-725 (in Japanese).
Ikeno, M., M. Matsuyama, T. Sakakiyama and K. Yanagisawa (2005): Empirical Research on
Assessment of Tsunami Wave Force Acting on breakwater Accompanied by Soliton Fission
and Breakers, Annual Journal of Coastal Engineering, JSCE, Vol. 52, pp. 751-755 (in Japanese).
Ikeno, M., M. Matsuyama, Tsutomu Sakakiyama and Ken Yanagisawa (2006): Experimental sutudy
on Soliton Fission Tsunami Wave Force which Running up on Land, Annual Journal of Coastal
Engineering, JSCE, Vol. 53, pp. 776-780 (in Japanese).
Ikeno, M., T. Yoshii, M. Matsuyama and N. Fujii (2009): Estimation of Pickup Rate of Suspended
Sand by Tsunami Experiment and Proposal of Pickup Rate Formula, Journal of the Japan
Society of Civil Engineers, Ser. B2 (Coastal Engineering), Vol. 65, No.1, pp. 506-510 (inJapanese).
Ikeno, M., N. Kihara and D. Takabatake (2013): Simple and Practical Estimation of Movement
140

Possibility and Collision Force of Debris due to Tsunami, Journal of the Japan Society of Civil
Engineers, Ser. B2 (Coastal Engineering), Vol.69, No.2, pp. I_861-I_865 (in Japanese).
Imai, K., D. Sugahara, T. Takahashi, S. Iwama and H. Tanaka (2015): Numerical Study for SedimentTransport due to Tsunami Around the Kitakami River Mouth, Journal of the Japan Society of
Civil Engineers, Ser. B2 (Coastal Engineering), Vol. 71, No. 2, pp. I_247-I_252 (in Japanese).
Imamura, F., I. Yoshida and A. Moore (2001): Numerical Study on the 1771 Meiwa Tsunami at
Ishigaki Island and the Movement of the Tsunami Stones, Tsunami Engineering Report, No.
18, pp. 61-72 (in Japanese).
Imazu, Y., F. Imamura and N. Shuto (1996): Study on the Stability Condition at a Front for Flood
Simulations, Japan Society of Civil Engineers 51st Annual Meeting Proceedings Part 2, pp.
242-243 (in Japanese).
Iwasaki, T. and Y. Zemin (1974): Numerical Experiments of Sanriku Big Tsunami, Proceedings of the
21st Japanese Conference on Coastal Engineering, pp. 83-89 (in Japanese).
Iwasaki, T. and A Mano (1979): Two-Dimensional Numerical Computation of Tsunami Run-ups in the
Eulerian Description, Proceedings of the 26th Japanese Conference on Coastal Engineering, pp.
70-74 (in Japanese).
Iwasaki, T., A. Mano and T. Arai (1981): Numerical Calculation of Tsunami at Ayasato-Minato,
Proceedings of the 28th Japanese Conference on Coastal Engineering, pp. 79-83 (in Japanese).
Iwase, H., T. Mikami and C. Goto (1998): Practical Tsunami Numerical Simulation Model by Use of
Non-linear Dispersive Long Wave Theory, Journal of Hydraoulic, Coastal and Environmental
Engineering, JSCE, No. 600/II-44, pp. 119-124 (in Japanese).
Iwase, H., C. Goto, K. Fujima and K. Iida (2002): The Dispersion Effect on the Propagation of Tsunami
in Deep Sea Region, Journal of Hydraoulic, Coastal and Environmental Engineering, JSCE,
No. 705/II-59, pp. 101-114 (in Japanese).
Japan Society of Civil Engineers, Editor (1999): Hydraulic Formula (1999 Edition), pp. 373-377 (inJapanese).
Japan Society of Civil Engineers Nuclear Civil Engineering Committee (2002): Tsunami Assessment
Method for Nuclear Power Plants in Japan (in Japanese).
Kawamata, K., K. Takaoka, K. Ban, F. Imamura, S. Yamaki and E. Kobayashi (2005): MODEL OFTSUNAMI GENERATION BY COLLAPSE OF VOLCANIC ERUPTION: THE 1741
OSHIMA-OSHIMA TSUNAMI, Tsunamis: Case Studies and Recent Developments, pp. 7996.
Kawasaki, K., S. Yamaguchi, M. Hakamata, N. Mizutani and S. Miyajima (2006): Wave Pressure
Acting on Drifting Body after Collision with Bore, Annual Journal of Coastal Engineering,
JSCE, Vol. 53, pp. 786-790 (in Japanese).
Kawasaki, K. and M. Hakamata (2007): Development of Three-Dimensional Numerical Model of141

Multiphase Flow “DOLPHIN-3D” and Dynamic Analysis of Drifting Bodies under Wave
Actions, Annual Journal of Coastal Engineering, JSCE, Vol. 54, pp. 31-35.
Kawasaki, K., S. Matsuura and T. Sakatani (2013): Validation of Free Surface Analysis Method inThree-Dimensional Computational Fluid Dynamics Tool “OpenFOAM”, Journal of the Japan
Society of Civil Engineers, Ser. B3 (Ocean Engineering) Vol. 69, No. 2, pp. I_748-I_753 (inJapanese).
Kihara, N. and M. Matsuyama (2010): On applicability of the hydrostatic 3-D tsunami analysis system
to tsunami-induced sediment transport - Simulations of sediment transport around the Kirinda
port induced by the Indian Ocean tsunami -, Central Research Institute of Electric Power
Industry Reports, N09004 (in Japanese).
Kihara, N., N. Fujii and M. Matsuyama (2012): Three-dimensional sediment transport processes ontsunami-induced topography changes in a harbor, Earth Planets Space, Vol. 64, pp. 787-797.
Kihara, N., D. Takabatake, T. Yoshii, M. Ikeno, K. Ota and N. Tanaka (2012): Tsunami Fluid Force on
Land Structures (Part I) - Numerical Study for Structures with Finite Width Under NonOverflow Condition -, Central Research Institute of Electric Power Industry Reports, N12010(in Japanese).
Kihara, N., M. Matsuyama and N. Fujii (2013): A Probabilistic Approach for Debris Impact Risk with
Numerical Simulations of Debris Behaviors, Journal of the Japan Society of Civil Engineers,
Ser. B2 (Coastal Engineering), Vol. 69, No. 2, pp. I_341-I_345 (in Japanese).
Kobayashi, A., Y. Oda, T. Toue, M. Takao and N. Fujii (1996): Research on Sediment Transport due
to Tsunamis, Proceedings of Coastal Engineering, JSCE, Vol. 43, pp. 691-695 (in Japanese).
Kobayashi, E., S. Koshimura and M. Kubo (2005): A Basic Study on Ship Drifting by Tsunami, Journalof the Kansai Society of Naval Architects, Japan, No. 243, pp. 49-56 (in Japanese).
Kotani, M., F. Imamura and N. Shuto (1998): Tsunami Run-up Simulation and Damage Estimation byusing GIS, Proceedins of Coastal Engineering, JSCE, Vol. 45, pp. 356-360 (in Japanese).
Kuriki, M., T. Suetsugi, H. Umino, Y. Tanaka and H. Kobayashi (1996): Flood Simulation Manual(Draft), Public Works Research Institute Document No. 3400, p. 137 (in Japanese).
Mansinha, L. and D. E. Smylie (1971): THE DISPLACEMENT FIELD OF INCLINED FAULTS,
Bulletin of the Seismological Society of America, Vol. 61, No. 5, pp. 1433-1440.
Ministry of Land, Infrastructure, Transport and Tourism National Institute for Land and InfrastructureManagement (2012): Practical Guide on Requirement for Structural Design of Tsunami
Evacuation Buildings, Technical Note National Institute for Land and InfrastructureManagement, No. 673 (in Japanese).
Ministry of Land, Infrastructure, Transport and Tourism Ports and Harbours Bureau (2013): TsunamiResistant Design Guideline for Breakwaters, 35 p. (in Japanese).
Mizutani, S. and F. Imamura (2000): Experiments with Bore Wave Force Acting on Structures,142Proceedings of Coastal Engineering, JSCE, Vol. 47, pp. 946-950 (in Japanese).
Mizutani, S. and F. Imamura (2002): Proposal for Design External Force Calculation Flowchart Taking
into Consideration Overflow and Impulsivity of Tsunami Bore, Proceedings of Coastal
Engineering, JSCE, Vol. 49, pp. 731-735 (in Japanese).
Morishita, Y. and T. Takahashi (2014): Accuracy Improvement of Movable Bed Model for Tsunamis
by Applying for Kesennuma Bay when the 2011 Tohoku Tsunami Arrived, Journal of the Japan
Society of Civil Engineers, Ser. B2 (Coastal Engineering), Vol. 70, pp. 491-495 (in Japanese).
Nakagawa, T. and Y. Koyanagi (1991): Experimental Data Analysis Using Least Squares Method,
University of Tokyo Press, 206p. (in Japanese).
Nishimura, Y. and H. Shimizu (1993): Tsunamis Generated by Eruptions from Komagatake Volcano,
Hokkaido, Japan, Bulletin of the Natural Disaster Science Data Center, Hokkaido, Vol. 8, pp.
17-28 (in Japanese).
Nuclear Civil Engineering Committee Tsunami Evaluation Subcommittee (2007): Research forDeveloping Precise Tsunami Evaluation Methods, Japan Society of Civil Engineers, Ser. B,
Vol. 63, No. 2, pp. 168-177 (in Japanese).
Ohtani, H., M. Sakai, K. Ishino, S. Arakawa and N. Mizumukai (1998): A Control Method of Surging
in Discharge Channel with Vertical Shafts, Anuual Journal of Hydraulic Engineering, JSCE,
Vol. 42, pp. 667-672 (in Japanese).
Okada, Y. (1985): SURFACE DEFORMATION DUE TO SHEAR AND TENSILE FAULTS IN A
HALF-SPACE, Bulletin of the Seismological Society of America, Vol. 75, No. 4, pp. 11351154.
Omori, M., N. Fujii, O. Kyoya, M. Takao, Toshimichi Kaneto and Tsuyoshi Ikeya (2000): Numerical
Simulation of Tsunami Water Level, Flow Velocity and Wave Force Overflowing Vertical
Seawalls, Proceedings of Coastal Engineering, JSCE, Vol. 47, pp. 376-380 (in Japanese).
OpenFOAM Foundation: OpenFOAM User Guide.
http://www.openfoam.org/docs/ (Accessed on April 2016)
Pham Van Phuc., M. Hasebe and I. Takahashi (2012): A Study on Three-Dimensional Tsunami
Analysis Using VOF Method, Journal of the Japan Society of Civil Engineers, Ser. B2 (Coastal
Engineering), Vol. 68, No. 2, pp. I_071-I_075 (in Japanese).
Rubey, W. (1933): SETTLING VELOCITY OF GRAVEL, SAND, AND SILT PARTICLES,
American Journal of Science, Vol. 25, pp. 325-338.
Sakakiyama, T. (2012): Tsunami Inundation Flow and Tsunami Pressure on Structures, Journal of theJapan Society of Civil Engineers, Ser. B2 (Coastal Engineering), Vol. 68, No. 2, pp. I_771I_775 (in Japanese).
Sasahara, N. (2004): Numerical Simulation of the Tsunami Caused by the Sector Collapse of Mt.
Mayuyama, Shimabara Peninsula, Kyushu in 1792, Report of Hydrographic and143

Oceanographic Researches, Vol. 40, pp. 63-72 (in Japanese).
Satake, K. (1987): INVERSION OF TSUNAMI WAVEFORMS FOR THE ESTIMATION OF A
FAULT HETEROGENEITY: METHOD AND NUMERICAL EXPERIMENTS, Journal of
Physics of the Earth, Vol. 35, pp. 241-254.
Satake, K. and Y. Kato, (2001): The 1741 Oshima-Oshima Eruption: Extent and Volume of Submarine
Debris Avalanche, Geophysical Research Letters, Vol. 28, No. 3, pp. 427-430.
Satake, K. and Y. Kato (2002): The 1741 Japan Sea tsunami caused by debris avalanche in the Oshima
Oshima volcano, Kaiyo Monthly Special Edition, No. 28, pp. 150-160 (in Japanese).Satake, K.
(2007): Volcanic origin of the 1741 Oshima-Oshima tsunami in the Japan Sea, Earth Planets
Space, Vol. 59, pp. 381-390.
Satake, K., Y. Fujii, T. Harada and Y. Namegaya (2013): Time and Space Distribution of Coseismic
Slip of the 2011 Tohoku Earthquake as Inferred from Tsunami Waveform Data, Bulletin of the
Seismological Society of America, Vol. 103, No. 2B, pp. 1473-1492.
Shuto, N. (1986): Tsunamis and Countermeasures, Proceedings of the Japan Society of Civil Engineers,
No. 369/II-5, pp. 1-11 (in Japanese).
Sugino, H., Changjiang Wu, M. Korenaga, M. Nemoto, Y. Iwabuchi and K. Ebisawa (2013): Analysis
and Verification of the 2011 Tohoku Earthquake Tsunami at Nuclear Power Plant Sites, Journalof Japan Association for Earthquake Engineering , Vol. 13, No. 2, pp. 2-21 (in Japanese).
Takabatake, D., N. Kihara and N. Tanaka (2013): Numerical Study for the Hydrodynamic Pressure on
the Front of Onshore Structures by Tsunami, Journal of the Japan Society of Civil Engineers,
Ser. B2 (Coastal Engineering), Vol. 69, No. 2, pp. I_851-I_855 (in Japanese).
Takahashi, T., F. Imamura and N. Shuto (1992): Numerical Simulation of Topographical Change due
to Tsunamis, Proceedings of Coastal Engineering, JSCE, Vol. 39, pp. 231-235 (in Japanese).
Takahashi, T., N. Shuto, F. Imamura and D. Asai (1999): A Movable Bed Model for Tsunami with
Exchange Rate between Bed Load Layer and Suspended, Proceedings of Coastal Engineering,
JSCE, Vol. 46, pp. 606-610 (in Japanese).
Takahashi, T., T. Kurokawa, M. Fujita and H. Shimada (2011): Hydraulic Experiment on SedimentTransport due to Tsunamis with Various Sand Grain Size, Journal of the Japan Society of Civil
Engineers, Ser. B2 (Coastal Engineering), Vol. 67, No. 2, pp. I_231-I_235 (in Japanese).
Takahashi, K. and T. Tomita (2013): Simulation of the 2011 Tohoku Tsunami in Kuji Bay Using ThreeDimensional Non-Hydrostatic Numerical Model, Journal of the Japan Society of Civil
Engineers, Ser. B2 (Coastal Engineering), Vol. 69, No. 2, pp. I_166-I_170 (in Japanese).
Takao, M., T. Tani, T. Kaneto, K. Yanagisawa and T. Annaka (2012): TSUNAMI INVERSIONANALYSIS OF THE GREAT EAST JAPAN EARTHQUAKE, Proceedings of theInternational Symposium on Engineering Lessons Learned from the 2011 Great East Japan
Earthquake, pp. 622-631.
144

Tanaka, H. (1985): Development of Mathematical Models for Tsunami Behavior on Coastal Zones,Central Research Institute of Electric Power Industry Reports, 385017, 46p. (in Japanese).
Tanimoto, K., H. Tsuruya and S. Nakano (1984): Study on Tsunami Force and Causes for Damage ofreclamation revetment at Nihonkai-Chubu Earthquake in 1983, Proceedings of the 31st
Japanese Conference on Coastal Engineering, pp. 257-261 (in Japanese).
Tanioka, Y. and K. Satake (1996): Tsunami generation by horizontal displacement of ocean bottom,
Geophysical Research Letters, Vol. 23, No. 8, pp. 861-864.
Tanioka, Y. and T. Baba (2004): Re-Estimation of Slip Distribution of the 1944 Tonankai Earthquake
using the Tsunami Waveform Inversion, The Earth Monthly, Vol. 26, No. 11, pp. 755-758 (inJapanese).
Tomita, T. and T. Kakinuma (2005): Storm Surge and Tsunami Simulator in Oceans and Coastal Areas(STOC), Report of the Port and Airport Research Institute, Vol. 44, No. 2, pp. 83-98 (inJapanese).
Tomita, T. and K Honda (2008): Application of Three-dimensional Non-hydrostatic Numerical Modelto Tsunamis in Coastal Areas, Annual Journal of Coastal Engineering, JSCE, Vol. 55, pp. 231235 (in Japanese).
Tsubaki, T. (1974): Encyclopedia of Fundamental Civil Engineering Studies 7: Hydraulics II, 16p. (inJapanese).
Tsuchiya, S., Y. Sato, M. Matsuyama and Y. Tanaka (2013): The Effect Generated by Calculation
Method of the Sea Bottom Displacement on Tsunami Estimation: Three-dimensional Sea
Bottom Crustal Movement Analysis, Journal of the Japan Society of Civil Engineers, Ser. B2(Coastal Engineering), Vol. 69, No. 2, pp. I_441-I_445 (in Japanese).
Watts, P., S. T. Grilli, D. R. Tappin and G. J. Fryer (2005): Tsunami Generation by Submarine Mass
Failure II: Predictive Equations and Case Studies, Journal of Waterway, Port, Coastal, andOcean Engineering, Vol. 131, No. 6, pp. 298-310.
Yanagisawa, H., N. Fujii and T. Kaneto (2012): Study on Characteristics of the 1700 Cascadia
Earthquake Tsunami along the Pacific Coast of Japan, Journal of the Japan Society of Civil
Engineers, Ser. B2 (Coastal Engineering), Vol. 69, No. 2, pp. I_441-I_445 (in Japanese).
Yoneyama, N., H. Nagashima and K. Toda (2008): Numerical Analysis for the Behavior of the Driftage
with Tsunami Run-up Using FAVOR Method, Annual Journal of Hydraulic Engineering, JSCE,
Vol. 52, pp. 1399-1404 (in Japanese).
Yoneyama, N. and H. Nagashima (2009): Development of a Three Dimensional Numerical Analysis
Method for the Drift Behavior in Tsunami, Journal of the Japan Society of Civil Engineers, Ser.
B2 (Coastal Engineering), Vol. B2-65, No. 1, pp. 266-270 (in Japanese).

145